{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T09:57:12Z","timestamp":1773309432815,"version":"3.50.1"},"reference-count":97,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2001,11,1]],"date-time":"2001-11-01T00:00:00Z","timestamp":1004572800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2001,11,1]],"date-time":"2001-11-01T00:00:00Z","timestamp":1004572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Computational Mathematics"],"published-print":{"date-parts":[[2001,11]]},"DOI":"10.1023\/a:1014246117321","type":"journal-article","created":{"date-parts":[[2002,12,29]],"date-time":"2002-12-29T19:13:07Z","timestamp":1041189187000},"page":"139-191","source":"Crossref","is-referenced-by-count":105,"title":["Adaptive Numerical Treatment of Elliptic Systems on Manifolds"],"prefix":"10.1007","volume":"15","author":[{"given":"M.","family":"Holst","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"388481_CR1","volume-title":"Sobolev Spaces","author":"R.A. Adams","year":"1978","unstructured":"R.A. Adams, Sobolev Spaces (Academic Press, San Diego, CA, 1978)."},{"key":"388481_CR2","volume-title":"Adaptive multilevel numerical methods","author":"B. Aksoylu","year":"2001","unstructured":"B. Aksoylu, Adaptive multilevel numerical methods, Ph.D. thesis, Department of Mathematics, UC San Diego (2001)."},{"issue":"2","key":"388481_CR3","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/S1064827597323373","volume":"22","author":"D. Arnold","year":"1997","unstructured":"D. Arnold, A. Mukherjee and L. Pouly, Locally adapted tetrahedral meshes using bisection, SIAM J. Sci. Comput. 22(2) (1997) 431\u2013448.","journal-title":"SIAM J. Sci. Comput."},{"key":"388481_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5734-9","volume-title":"Nonlinear Analysis on Manifolds. Monge-Amp\u00e9re Equations","author":"T. Aubin","year":"1982","unstructured":"T. Aubin, Nonlinear Analysis on Manifolds. Monge-Amp\u00e9re Equations (Springer, New York, 1982)."},{"key":"388481_CR5","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1002\/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N","volume":"40","author":"I. Babu\u0161ka","year":"1997","unstructured":"I. Babu\u0161ka and J.M.Melenk, The partition of unity finite element method, Internat. J. Numer.Methods Engrg. 40 (1997) 727\u2013758.","journal-title":"Internat. J. Numer.Methods Engrg."},{"key":"388481_CR6","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1137\/0715049","volume":"15","author":"I. Babu\u0161ka","year":"1978","unstructured":"I. Babu\u0161ka and W. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736\u2013754.","journal-title":"SIAM J. Numer. Anal."},{"key":"388481_CR7","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1002\/nme.1620121010","volume":"12","author":"I. Babu\u0161ka","year":"1978","unstructured":"I. Babu\u0161ka and W. Rheinboldt, A posteriori error estimates for the finite element method, Internat. J. Numer. Methods Engrg. 12 (1978) 1597\u20131615.","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"388481_CR8","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1002\/1096-987X(20001130)21:15<1343::AID-JCC2>3.0.CO;2-K","volume":"21","author":"N. Baker","year":"2000","unstructured":"N. Baker, M. Holst and F. Wang, Adaptive multilevel finite element solution of the Poisson-Boltzmann equation II: Refinement at solvent accessible surfaces in biomolecular systems, J. Comput. Chem. 21 (2000) 1343\u20131352.","journal-title":"J. Comput. Chem."},{"issue":"4","key":"388481_CR9","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1137\/S1064827599353701","volume":"22","author":"R. Bank","year":"2000","unstructured":"R. Bank and M. Holst, A new paradigm for parallel adaptive mesh refinement, SIAM J. Sci. Statist. Comput. 22(4) (2000) 1411\u20131443.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"388481_CR10","series-title":"Software, Environments and Tools","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719635","volume-title":"PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, Users' Guide 8.0","author":"R.E. Bank","year":"1998","unstructured":"R.E. Bank, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, Users' Guide 8.0, Software, Environments and Tools, Vol. 5. (SIAM, Philadelphia, PA, 1998)."},{"issue":"153","key":"388481_CR11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1090\/S0025-5718-1981-0595040-2","volume":"36","author":"R.E. Bank","year":"1981","unstructured":"R.E. Bank and T.F. Dupont, An optimal order process for solving finite element equations, Math. Comp. 36(153) (1981) 35\u201351.","journal-title":"Math. Comp."},{"key":"388481_CR12","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF01462238","volume":"52","author":"R.E. Bank","year":"1988","unstructured":"R.E. Bank, T.F. Dupont and H. Yserentant, The hierarchical basis multigrid method, Numer. Math. 52 (1988) 427\u2013458.","journal-title":"Numer. Math."},{"key":"388481_CR13","unstructured":"R.E. Bank, M. Holst, B. Mantel, J. Periaux and C.H. Zhou, CFD PPLTMG: Using a posteriori error estimates and domain decomposition, in: ECCOMAS 98, New York, 1998."},{"key":"388481_CR14","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0377-0427(89)90148-9","volume":"26","author":"R.E. Bank","year":"1989","unstructured":"R.E. Bank and H.D.Mittelmann, Stepsize selection in continuation procedures and damped Newton's method, J. Comput. Appl. Math. 26 (1989) 67\u201377.","journal-title":"J. Comput. Appl. Math."},{"issue":"6","key":"388481_CR15","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1137\/0717068","volume":"17","author":"R.E. Bank","year":"1980","unstructured":"R.E. Bank and D.J. Rose, Parameter selection for Newton-like methods applicable to nonlinear partial differential equations, SIAM J. Numer. Anal. 17(6) (1980) 806\u2013822.","journal-title":"SIAM J. Numer. Anal."},{"key":"388481_CR16","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF01398257","volume":"37","author":"R.E. Bank","year":"1981","unstructured":"R.E. Bank and D.J. Rose, Global approximate Newton methods, Numer. Math. 37 (1981) 279\u2013295.","journal-title":"Numer. Math."},{"issue":"160","key":"388481_CR17","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1090\/S0025-5718-1982-0669639-X","volume":"39","author":"R.E. Bank","year":"1982","unstructured":"R.E. Bank and D.J. Rose, Analysis of a multilevel iterative method for nonlinear finite element equations, Math. Comp. 39(160) (1982) 453\u2013465.","journal-title":"Math. Comp."},{"issue":"4","key":"388481_CR18","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1137\/0730048","volume":"30","author":"R.E. Bank","year":"1993","unstructured":"R.E. Bank and R.K. Smith, A posteriori error estimates based on hierarchical bases, SIAM J. Numer. Anal. 30(4) (1993) 921\u2013935.","journal-title":"SIAM J. Numer. Anal."},{"key":"388481_CR19","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1137\/S0036142994265292","volume":"34","author":"R.E. Bank","year":"1997","unstructured":"R.E. Bank and R.K. Smith, Mesh smoothing using a posteriori error estimates, SIAM J. Numer. Anal. 34 (1997) 979\u2013997.","journal-title":"SIAM J. Numer. Anal."},{"issue":"170","key":"388481_CR20","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1090\/S0025-5718-1985-0777265-X","volume":"44","author":"R.E. Bank","year":"1985","unstructured":"R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44(170) (1985) 283\u2013301.","journal-title":"Math. Comp."},{"key":"388481_CR21","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0377-0427(91)90224-8","volume":"36","author":"E. B\u00e4nsch","year":"1991","unstructured":"E. B\u00e4nsch, An adaptive finite-element strategy for the three-dimsional time-dependent Navier-Stokes equations, J. Comput. Appl. Math. 36 (1991) 3\u201328.","journal-title":"J. Comput. Appl. Math."},{"key":"388481_CR22","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0899-8248(91)90006-G","volume":"3","author":"E. B\u00e4nsch","year":"1991","unstructured":"E. B\u00e4nsch, Local mesh refinement in 2 and 3 dimensions, Impact of Computing in Science and Engineering 3 (1991) 181\u2013191.","journal-title":"Impact of Computing in Science and Engineering"},{"key":"388481_CR23","series-title":"Technical Report","volume-title":"A posteriori error estimation for nonlinear problems by duality techniques","author":"E. B\u00e4nsch","year":"1995","unstructured":"E. B\u00e4nsch and K.G. Siebert, A posteriori error estimation for nonlinear problems by duality techniques, Technical Report, Institut f\u00fcr Angewandte Mathematik, Freiburg, Germany (1995)."},{"key":"388481_CR24","doi-asserted-by":"crossref","unstructured":"P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuss, H. Rentz-Reichert and C. Wieners, UG-A flexible software toolbox for solving partial differential equations (1998).","DOI":"10.1007\/s007910050003"},{"key":"388481_CR25","series-title":"Technical Report TR95-4","volume-title":"KASKADE 3.0: An object-oriented adaptive finite element code","author":"R. Beck","year":"1995","unstructured":"R. Beck, B. Erdmann and R. Roitzsch, KASKADE 3.0: An object-oriented adaptive finite element code, Technical Report TR95-4, Konrad-Zuse-Zentrum for Informationstechnik, Berlin (1995)."},{"key":"388481_CR26","unstructured":"J. Bey, Adaptive Grid Manager: AGM3D Manual, Technical Report 50, SFB 382, Math. Inst., University of Tubingen, 1996."},{"key":"388481_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4338-8","volume-title":"The Mathematical Theory of Finite Element Methods","author":"S.C. Brenner","year":"1994","unstructured":"S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods (Springer, New York, 1994)."},{"key":"388481_CR28","unstructured":"F. Brezzi, Mathematical theory of finite elements, in: State-of-the-Art Surveys on Finite Element Technology, eds. A.K. Noor and W.D. Pilkey (New York, 1985) pp. 1\u201325."},{"key":"388481_CR29","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/BF01404345","volume":"28","author":"F. Brezzi","year":"1977","unstructured":"F. Brezzi, W.W. Hager and P.A. Raviart, Error estimates for the finite element solution of variational inequalities, Numer. Math. 28 (1977) 431\u2013443.","journal-title":"Numer. Math."},{"key":"388481_CR30","unstructured":"T. Chan, S. Go, and L. Zikatanov, Lecture notes on multilevel methods for elliptic problems on unstructured meshes, Technical Report, Department of Mathematics, UCLA (1997)."},{"key":"388481_CR31","unstructured":"T.F. Chan, B. Smith and J. Zou, Overlapping Schwarz methods on unstructured meshes using nonmatching coarse grids, Technical Report CAM 94-8, Department of Mathematics, UCLA (1994)."},{"key":"388481_CR32","first-page":"349","volume":"315","author":"Y. Choquet-Bruhat","year":"1992","unstructured":"Y. Choquet-Bruhat, J. Isenberg and V. Moncrief, Solutions of constraints for Einstein equations, C. R. Acad. Sci. Paris 315 (1992) 349\u2013355.","journal-title":"C. R. Acad. Sci. Paris"},{"key":"388481_CR33","volume-title":"General Relativity and Gravitation","author":"Y. Choquet-Bruhat","year":"1980","unstructured":"Y. Choquet-Bruhat and J.W. York, Jr., The Cauchy problem, in: General Relativity and Gravitation, ed. A. Held (Plenum, New York, 1980)."},{"key":"388481_CR34","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1978","unstructured":"P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, New York, 1978)."},{"key":"388481_CR35","first-page":"77","volume":"2","author":"P. Cl\u00e8ment","year":"1975","unstructured":"P. Cl\u00e8ment, Approximation by finite element functions using local regularization, RAIRO 2 (1975) 77\u201384.","journal-title":"RAIRO"},{"key":"388481_CR36","doi-asserted-by":"crossref","unstructured":"W. Dahmen, Smooth piecewise quadratic surfaces, in: Mathematical Methods in Computer-Aided Geometric Design (1989) pp. 181\u2013193.","DOI":"10.1016\/B978-0-12-460515-2.50017-2"},{"issue":"2","key":"388481_CR37","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0167-8396(84)90025-6","volume":"18","author":"W. Dahmen","year":"1984","unstructured":"W. Dahmen and C. Micchelli, Subdivision algorithms for the generation of box spline surfaces, Computer-Aided Geom. Design 18(2) (1984) 115\u2013129.","journal-title":"Computer-Aided Geom. Design"},{"key":"388481_CR38","volume-title":"Interpolation and Approximation","author":"P.J. Davis","year":"1963","unstructured":"P.J. Davis, Interpolation and Approximation (Dover Publications, New York, 1963)."},{"issue":"2","key":"388481_CR39","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1137\/0719025","volume":"19","author":"R.S. Dembo","year":"1982","unstructured":"R.S. Dembo, S.C. Eisenstat and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal. 19(2) (1982) 400\u2013408.","journal-title":"SIAM J. Numer. Anal."},{"key":"388481_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02888-9","volume-title":"Constructive Approximation","author":"R.A. DeVore","year":"1993","unstructured":"R.A. DeVore and G.G. Lorentz, Constructive Approximation (Springer, New York, 1993)."},{"key":"388481_CR41","unstructured":"S.C. Eisenstat and H.F. Walker, Globally convergent inexact Newton methods, Technical Report, Department of Mathematics and Statistics, Utah State University (1992)."},{"key":"388481_CR42","unstructured":"D. Estep, M. Holst and D. Mikulencak, Accounting for stability: A posteriori error estimates for finite element methods based on residuals and variational analysis, to appear, in Communications in Numerical Methods in Engineering."},{"key":"388481_CR43","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1090\/S0025-5718-1974-0391502-8","volume":"28","author":"R. Falk","year":"1974","unstructured":"R. Falk, Error estimates for the approximation of a class of variational inequalities, Math. Comp. 28 (1974) 963\u2013971.","journal-title":"Math. Comp."},{"key":"388481_CR44","volume-title":"Nonlinear Differential Equations","author":"S. Fucik","year":"1980","unstructured":"S. Fucik and A. Kufner, Nonlinear Differential Equations (Elsevier Science, New York, 1980)."},{"issue":"3","key":"388481_CR45","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1137\/S1064827599355840","volume":"22","author":"M. Griebel","year":"2000","unstructured":"M. Griebel and M.A. Schweitzer, A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic PDEs, SIAM J. Sci. Statist. Comput. 22(3) (2000) 853\u2013890.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"388481_CR46","unstructured":"C. Grimm, Modeling surfaces of arbitrary topology using manifolds, Ph.D. thesis, Department of Computer Science, Brown University (1996)."},{"issue":"4","key":"388481_CR47","first-page":"359","volume":"29","author":"C. Grimm","year":"1995","unstructured":"C. Grimm and J. Hughes, Modeling surfaces of arbitrary topology using manifolds, in: Graphics (Proceedings of SIGGRAPH 95), SIGGRAPH 29(4) (1995) 359\u2013369.","journal-title":"SIGGRAPH"},{"key":"388481_CR48","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02427-0","volume-title":"Multi-grid Methods and Applications","author":"W. Hackbusch","year":"1985","unstructured":"W. Hackbusch, Multi-grid Methods and Applications (Springer, Berlin, 1985)."},{"key":"388481_CR49","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4288-8","volume-title":"Iterative Solution of Large Sparse Systems of Equations","author":"W. Hackbusch","year":"1994","unstructured":"W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations (Springer, Berlin, 1994)."},{"key":"388481_CR50","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511524646","volume-title":"The Large Scale Structure of Space-Time","author":"S.W. Hawking","year":"1973","unstructured":"S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time (Cambridge Univ. Press, Cambridge, 1973)."},{"key":"388481_CR51","volume-title":"Sobolev Spaces on Riemannian Manifolds","author":"E. Hebey","year":"1991","unstructured":"E. Hebey, Sobolev Spaces on Riemannian Manifolds (Springer, Berlin, 1991)."},{"key":"388481_CR52","unstructured":"M. Holst, Finite element approximation theory on Riemannian manifolds (in preparation)."},{"key":"388481_CR53","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1002\/1096-987X(20001130)21:15<1319::AID-JCC1>3.0.CO;2-8","volume":"21","author":"M. Holst","year":"2000","unstructured":"M. Holst, N. Baker and F. Wang, Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I: Algorithms and examples, J. Comput. Chem. 21 (2000) 1319\u20131342.","journal-title":"J. Comput. Chem."},{"key":"388481_CR54","unstructured":"M. Holst and D. Bernstein, Some results on non-constant mean curvature solutions to the Einstein constraint equations (in preparation)."},{"key":"388481_CR55","unstructured":"M. Holst and D. Bernstein, Adaptive finite element solution of the initial value problem in general relativity I. Algorithms (in preparation)."},{"key":"388481_CR56","series-title":"Contemporary Mathematics","volume-title":"Recent Developments in Optimization Theory and Nonlinear Analysis","author":"M. Holst","year":"1997","unstructured":"M. Holst and E. Titi, Determining projections and functionals for weak solutions of the Navier-Stokes equations, in: Recent Developments in Optimization Theory and Nonlinear Analysis, eds. Y. Censor and S. Reich, Contemporary Mathematics, Vol. 204 (Amer. Math. Soc., Providence, RI, 1997)."},{"issue":"2","key":"388481_CR57","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1137\/S0036142994275743","volume":"34","author":"M. Holst","year":"1997","unstructured":"M. Holst and S. Vandewalle, Schwarz methods: to symmetrize or not to symmetrize, SIAM J. Numer. Anal. 34(2) (1997) 699\u2013722.","journal-title":"SIAM J. Numer. Anal."},{"key":"388481_CR58","doi-asserted-by":"crossref","first-page":"1819","DOI":"10.1088\/0264-9381\/13\/7\/015","volume":"13","author":"J. Isenberg","year":"1996","unstructured":"J. Isenberg, Constant mean curvature solutions of the Einstein constraint equations on closed manifolds, Classical Quantum Gravity 13 (1996) 1819\u20131847.","journal-title":"Classical Quantum Gravity"},{"key":"388481_CR59","doi-asserted-by":"crossref","first-page":"1819","DOI":"10.1088\/0264-9381\/13\/7\/015","volume":"13","author":"J. Isenberg","year":"1996","unstructured":"J. Isenberg and V. Moncrief, A set of nonconstant mean curvature solutions of the Einstein constraint equations on closed manifolds, Classical Quantum Gravity 13 (1996) 1819\u20131847.","journal-title":"Classical Quantum Gravity"},{"issue":"2","key":"388481_CR60","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1137\/0728023","volume":"28","author":"J.W. Jerome","year":"1991","unstructured":"J.W. Jerome and T. Kerkhoven, A finite element approximation theory for the drift diffusion semiconductor model, SIAM J. Numer. Anal. 28(2) (1991) 403\u2013422.","journal-title":"SIAM J. Numer. Anal."},{"key":"388481_CR61","volume-title":"Numerical Methods in Bifurcation Problems","author":"H.B. Keller","year":"1987","unstructured":"H.B. Keller, Numerical Methods in Bifurcation Problems (Tata Institute of Fundamental Research, Bombay, India, 1987)."},{"key":"388481_CR62","volume-title":"Numerical Methods for Two-Point Boundary-Value Problems","author":"H.B. Keller","year":"1992","unstructured":"H.B. Keller, Numerical Methods for Two-Point Boundary-Value Problems (Dover, New York, 1992)."},{"key":"388481_CR63","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/BF01386428","volume":"57","author":"T. Kerkhoven","year":"1990","unstructured":"T. Kerkhoven and J.W. Jerome, L\u221e stability of finite element approximations of elliptic gradient equations, Numer. Math. 57 (1990) 561\u2013575.","journal-title":"Numer. Math."},{"key":"388481_CR64","doi-asserted-by":"crossref","DOI":"10.1007\/b98852","volume-title":"Riemannian Manifolds","author":"J.M. Lee","year":"1997","unstructured":"J.M. Lee, Riemannian Manifolds (Springer, New York, 1997)."},{"key":"388481_CR65","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1007\/BF01955874","volume":"34","author":"A. Liu","year":"1994","unstructured":"A. Liu and B. Joe, Relationship between tetrahedron shape measures, BIT 34 (1994) 268\u2013287.","journal-title":"BIT"},{"issue":"6","key":"388481_CR66","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1137\/0916074","volume":"16","author":"A. Liu","year":"1995","unstructured":"A. Liu and B. Joe, Quality local refinement of tetrahedral meshes based on bisection, SIAM J. Sci. Statist. Comput. 16(6) (1995) 1269\u20131291.","journal-title":"SIAM J. Sci. Statist. Comput."},{"issue":"3","key":"388481_CR67","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1080\/01630569408816569","volume":"15","author":"J. Liu","year":"1994","unstructured":"J. Liu and W. Rheinboldt, A posteriori finite element error estimators for indefinite elliptic boundary value problems, Numer. Functional Anal. Optimiz. 15(3) (1994) 335\u2013356.","journal-title":"Numer. Functional Anal. Optimiz"},{"issue":"5","key":"388481_CR68","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1080\/01630569608816714","volume":"17","author":"J. Liu","year":"1996","unstructured":"J. Liu and W. Rheinboldt, A posteriori finite element error estimators for parametrized nonlinear boundary value problems, Numer. Functional Anal. Optimiz. 17(5) (1996) 605\u2013637.","journal-title":"Numer. Functional Anal. Optimiz."},{"key":"388481_CR69","volume-title":"Mathematical Foundations of Elasticity","author":"J.E. Marsden","year":"1994","unstructured":"J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity (Dover, New York, 1994)."},{"issue":"1","key":"388481_CR70","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1137\/0916014","volume":"16","author":"J. Maubach","year":"1995","unstructured":"J. Maubach, Local bisection refinement for N-simplicial grids generated by relection, SIAM J. Sci. Statist. Comput. 16(1) (1995) 210\u2013277.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"388481_CR71","volume-title":"Shapes and implementations in three-dimensional geometry","author":"E. Mucke","year":"1993","unstructured":"E. Mucke, Shapes and implementations in three-dimensional geometry, Ph.D. thesis, Department of Computer Science, University of Illinois at Urbana-Champaign (1993)."},{"key":"388481_CR72","unstructured":"A. Mukherjee, An adaptive finite element code for elliptic boundary value problems in three dimensions with applications in numerical relativity, Ph.D. thesis, Department of Mathematics, Pennsylvania State University (1996)."},{"key":"388481_CR73","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1090\/S0025-5718-1974-0373325-9","volume":"28","author":"J.A. Nitsche","year":"1974","unstructured":"J.A. Nitsche and A.H. Schatz, Interior estimates for Ritz-Galerkin methods, Math. Comp. 28 (1974) 937\u2013958.","journal-title":"Math. Comp."},{"issue":"2","key":"388481_CR74","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1103\/PhysRevD.10.428","volume":"10","author":"N. O. Murchadha","year":"1974","unstructured":"N. O. Murchadha and J. York, Jr., Initial-value problem of general relativity. I. General formulation and physical interpretation, Phys. Rev. D 10(2) (1974) 428\u2013436.","journal-title":"Phys. Rev. D"},{"issue":"2","key":"388481_CR75","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1103\/PhysRevD.10.437","volume":"10","author":"N. O. Murchadha","year":"1974","unstructured":"N. O. Murchadha and J. York, Jr., Initial-value problem of general relativity. II. Stability of solutions of the initial-value equations, Phys. Rev. D 10(2) (1974) 437\u2013446.","journal-title":"Phys. Rev. D"},{"issue":"11","key":"388481_CR76","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1063\/1.1666225","volume":"14","author":"N. O. Murchadha","year":"1973","unstructured":"N. O. Murchadha and J. York, Jr., Existence and uniqueness of solutions of the Hamiltonian constraint of general relativity on compact manifolds, J. Math. Phys. 14(11) (1973) 1551\u20131557.","journal-title":"J. Math. Phys."},{"key":"388481_CR77","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"J.M. Ortega","year":"1970","unstructured":"J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970)."},{"key":"388481_CR78","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1002\/nme.1620200412","volume":"20","author":"M. Rivara","year":"1984","unstructured":"M. Rivara, Algorithms for refining triangular grids suitable for adaptive and multigrid techniques, Internat. J. Numer. Methods Engrg. 20 (1984) 745\u2013756.","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"388481_CR79","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0377-0427(91)90227-B","volume":"36","author":"M. Rivara","year":"1991","unstructured":"M. Rivara, Local modification of meshes for adaptive and\/or multigrid finite-element methods, J. Comput. Appl. Math. 36 (1991) 79\u201389.","journal-title":"J. Comput. Appl. Math."},{"key":"388481_CR80","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1090\/S0025-5718-1975-0375068-5","volume":"29","author":"I. Rosenberg","year":"1975","unstructured":"I. Rosenberg and F. Stenger, A lower bound on the angles of triangles constructed by bisecting the longest side, Math. Comp. 29 (1975) 390\u2013395.","journal-title":"Math. Comp."},{"key":"388481_CR81","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511623783","volume-title":"The Laplacian on a Riemannian Manifold","author":"S. Rosenberg","year":"1997","unstructured":"S. Rosenberg, The Laplacian on a Riemannian Manifold (Cambridge Univ. Press, Cambridge, 1997)."},{"key":"388481_CR82","series-title":"Frontiers in Applied Mathematics","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1137\/1.9781611971057.ch4","volume-title":"Multigrid Methods","author":"J.W. Ruge","year":"1987","unstructured":"J.W. Ruge and K. St\u00fcben, Algebraic Multigrid (AMG), in: Multigrid Methods, Frontiers in Applied Mathematics, Vol. 3, ed. S.F. McCormick (SIAM, Philadelphia, PA, 1987) pp. 73\u2013130."},{"issue":"128","key":"388481_CR83","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1090\/S0025-5718-1974-0373326-0","volume":"28","author":"A.H. Schatz","year":"1974","unstructured":"A.H. Schatz, An Oberservation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp. 28(128) (1974) 959\u2013962.","journal-title":"Math. Comp."},{"key":"388481_CR84","first-page":"445","volume":"62","author":"A.H. Schatz","year":"2000","unstructured":"A.H. Schatz and J. Wang, Some new error estimates for Ritz-Galerkin methods with minimal regularity assumptions, Math. Comp. 62 (2000) 445\u2013475.","journal-title":"Math. Comp."},{"key":"388481_CR85","volume-title":"Hodge Decomposition: A Method for Solving Boundary Value Problems","author":"G. Schwarz","year":"1991","unstructured":"G. Schwarz, Hodge Decomposition: A Method for Solving Boundary Value Problems (Springer, New York, 1991)."},{"issue":"190","key":"388481_CR86","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0025-5718-1990-1011446-7","volume":"54","author":"L.R. Scott","year":"1990","unstructured":"L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54(190) (1990) 483\u2013493.","journal-title":"Math. Comp."},{"key":"388481_CR87","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1090\/S0025-5718-1980-0583497-1","volume":"35","author":"M. Stynes","year":"1980","unstructured":"M. Stynes, On faster convergence of the bisection method for all triangles, Math. Comp. 35 (1980) 1195\u20131201.","journal-title":"Math. Comp."},{"key":"388481_CR88","series-title":"Technical Report UCD\/CCM 34","volume-title":"Algebraic multigrid on unstructured meshes","author":"P. Vanek","year":"1994","unstructured":"P. Vanek, J. Mandel and M. Brezina, Algebraic multigrid on unstructured meshes, Technical Report UCD\/CCM 34, Center for Computational Mathematics, University of Colorado at Denver (1994)."},{"issue":"206","key":"388481_CR89","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1090\/S0025-5718-1994-1213837-1","volume":"62","author":"R. Verf\u00fcrth","year":"1994","unstructured":"R. Verf\u00fcrth, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math. Comp. 62(206) (1994) 445\u2013475.","journal-title":"Math. Comp."},{"key":"388481_CR90","volume-title":"A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques","author":"R. Verf\u00fcrth","year":"1996","unstructured":"R. Verf\u00fcrth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques (Wiley, New York, 1996)."},{"key":"388481_CR91","doi-asserted-by":"crossref","DOI":"10.7208\/chicago\/9780226870373.001.0001","volume-title":"General Relativity","author":"R.M. Wald","year":"1984","unstructured":"R.M. Wald, General Relativity (Univ. of Chicago Press, Chicago, IL, 1984)."},{"key":"388481_CR92","volume-title":"Partial Differential Equations","author":"J. Wloka","year":"1992","unstructured":"J. Wloka, Partial Differential Equations (Cambridge Univ. Press, Cambridge, 1992)."},{"issue":"4","key":"388481_CR93","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1137\/1034116","volume":"34","author":"J. Xu","year":"1992","unstructured":"J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Review 34(4) (1992) 581\u2013613.","journal-title":"SIAM Review"},{"key":"388481_CR94","unstructured":"J. Xu, A novel two-grid method for semilinear elliptic equations, Technical Report, Department of Mathematics, Penn State University (1992)."},{"key":"388481_CR95","unstructured":"J. Xu, Two-grid finite element discretization for nonlinear elliptic equations, Technical Report, Department of Mathematics, Penn State University (1992)."},{"key":"388481_CR96","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1090\/S0025-5718-99-01149-7","volume":"69","author":"J. Xu","year":"2000","unstructured":"J. Xu and A. Zhou, Local and parallel finite element algorithms based on two-grid discretizations, Math. Comp. 69 (2000) 881\u2013909.","journal-title":"Math. Comp."},{"key":"388481_CR97","volume-title":"Functional Analysis","author":"K. Yosida","year":"1980","unstructured":"K. Yosida, Functional Analysis (Springer, Berlin, 1980)."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014246117321.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1014246117321\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014246117321.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T23:16:24Z","timestamp":1747437384000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1014246117321"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11]]},"references-count":97,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2001,11]]}},"alternative-id":["388481"],"URL":"https:\/\/doi.org\/10.1023\/a:1014246117321","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,11]]}}}