{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:19:45Z","timestamp":1762917585279},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T00:00:00Z","timestamp":1427241600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1007\/s10915-015-0013-8","type":"journal-article","created":{"date-parts":[[2015,3,24]],"date-time":"2015-03-24T10:53:41Z","timestamp":1427194421000},"page":"67-90","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains"],"prefix":"10.1007","volume":"66","author":[{"given":"Yanlai","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sigal","family":"Gottlieb","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alfa","family":"Heryudono","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akil","family":"Narayan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,3,25]]},"reference":[{"key":"13_CR1","doi-asserted-by":"crossref","first-page":"525","DOI":"10.2514\/3.7539","volume":"16","author":"BO Almroth","year":"1978","unstructured":"Almroth, B.O., Stern, P., Brogan, F.A.: Automatic choice of global shape functions in structural analysis. AIAA J. 16, 525\u2013528 (1978)","journal-title":"AIAA J."},{"issue":"4","key":"13_CR2","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1006\/mssp.1996.0027","volume":"10","author":"E Balmes","year":"1996","unstructured":"Balmes, E.: Parametric families of reduced finite element models: theory and applications. Mach. Syst. Signal Process. 10(4), 381\u2013394 (1996)","journal-title":"Mach. Syst. Signal Process."},{"key":"13_CR3","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.crma.2004.08.006","volume":"339","author":"M Barrault","year":"2004","unstructured":"Barrault, M., Nguyen, N.C., Maday, Y., Patera, A.T.: An \u201cempirical interpolation\u201d method: application to efficient reduced-basis discretization of partial differential equations. C. R. Acad. Sci. Paris S\u00e9r I 339, 667\u2013672 (2004)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r I"},{"issue":"7","key":"13_CR4","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1002\/zamm.19950750709","volume":"75","author":"A Barrett","year":"1995","unstructured":"Barrett, A., Reddien, G.: On the reduced basis method. Z. Angew. Math. Mech. 75(7), 543\u2013549 (1995)","journal-title":"Z. Angew. Math. Mech."},{"issue":"19","key":"13_CR5","doi-asserted-by":"crossref","first-page":"7384","DOI":"10.1016\/j.jcp.2011.06.005","volume":"230","author":"V Bayona","year":"2011","unstructured":"Bayona, V., Moscoso, M., Kindelan, M.: Optimal constant shape parameter for multiquadric based RBF-FD method. J. Comput. Phys. 230(19), 7384\u20137399 (2011)","journal-title":"J. Comput. Phys."},{"issue":"9","key":"13_CR6","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1016\/j.enganabound.2012.03.010","volume":"36","author":"V Bayona","year":"2012","unstructured":"Bayona, V., Moscoso, M., Kindelan, M.: Gaussian RBF-FD weights and its corresponding local truncation errors. Eng. Anal. Bound. Elem. 36(9), 1361\u20131369 (2012)","journal-title":"Eng. Anal. Bound. Elem."},{"key":"13_CR7","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1137\/100795772","volume":"43","author":"P Binev","year":"2011","unstructured":"Binev, P., Cohen, A., Dahmen, W., Devore, R., Petrova, G., Wojtaszczyk, P.: Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43, 1457\u20131472 (2011)","journal-title":"SIAM J. Math. Anal."},{"key":"13_CR8","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1051\/m2an\/2011056","volume":"46","author":"A Buffa","year":"2011","unstructured":"Buffa, A., Maday, Y., Patera, A.T., Prud\u2019homme, C., Turinici, G.: A priori convergence of the greedy algorithm for the parametrized reduced basis. ESAIM Math. Model. Numer. Anal. 46, 595\u2013603 (2011). (Special Issue in honor of David Gottlieb)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"13_CR9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511543241","volume-title":"Radial Basis Functions: Theory and Implementations, Cambridge Monographs on Applied and Computational Mathematics","author":"MD Buhmann","year":"2003","unstructured":"Buhmann, M.D.: Radial Basis Functions: Theory and Implementations, Cambridge Monographs on Applied and Computational Mathematics, vol. 12. Cambridge University Press, Cambridge (2003)"},{"key":"13_CR10","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.jcp.2013.02.028","volume":"242","author":"K Carlberg","year":"2013","unstructured":"Carlberg, K., Farhat, C., Cortial, J., Amsallem, D.: The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows. J. Comput. Phys. 242, 623\u2013647 (2013)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"13_CR11","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s11075-014-9850-z","volume":"68","author":"R Cavoretto","year":"2015","unstructured":"Cavoretto, R., Fasshauer, G.E., McCourt, M.: An introduction to the Hilbert-Schmidt SVD using iterated Brownian bridge kernels. Numer. Algorithms 68(2), 393\u2013422 (2015)","journal-title":"Numer. Algorithms"},{"issue":"3","key":"13_CR12","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1007\/s10915-012-9654-z","volume":"55","author":"Y Chen","year":"2013","unstructured":"Chen, Y., Gottlieb, S.: Reduced collocation methods: reduced basis methods in the collocation framework. J. Sci. Comput. 55(3), 718\u2013737 (2013)","journal-title":"J. Sci. Comput."},{"issue":"7\u20138","key":"13_CR13","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.crma.2014.06.001","volume":"352","author":"Y Chen","year":"2014","unstructured":"Chen, Y., Gottlieb, S., Maday, Y.: Parametric analytical preconditioning and its applications to the reduced collocation methods. C. R. Math. 352(7\u20138), 661\u2013666 (2014)","journal-title":"C. R. Math."},{"key":"13_CR14","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1051\/m2an\/2009037","volume":"43","author":"Y Chen","year":"2009","unstructured":"Chen, Y., Hesthaven, J.S., Maday, Y., Rodr\u00edguez, J.: Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2d Maxwell\u2019s problem. Math. Modell. Numer. Anal. 43, 1099\u20131116 (2009)","journal-title":"Math. Modell. Numer. Anal."},{"issue":"2","key":"13_CR15","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1137\/09075250X","volume":"32","author":"Y Chen","year":"2010","unstructured":"Chen, Y., Hesthaven, J.S., Maday, Y., Rodr\u00edguez, J.: Certified reduced basis methods and output bounds for the harmonic Maxwell\u2019s equations. SIAM J. Sci. Comput. 32(2), 970\u2013996 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"13_CR16","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/S0898-1221(01)00295-4","volume":"43","author":"T Driscoll","year":"2002","unstructured":"Driscoll, T., Fornberg, B.: Interpolation in the limit of increasingly flat radial basis functions. Comput. Math. Appl. 43, 413\u2013422 (2002)","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"13_CR17","doi-asserted-by":"crossref","first-page":"A937","DOI":"10.1137\/10081157X","volume":"34","author":"M Drohmann","year":"2012","unstructured":"Drohmann, M., Haasdonk, B., Ohlberger, M.: Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation. SIAM J. Sci. Comput. 34(2), A937\u2013A969 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"13_CR18","doi-asserted-by":"crossref","first-page":"A737","DOI":"10.1137\/110824784","volume":"34","author":"GE Fasshauer","year":"2012","unstructured":"Fasshauer, G.E., McCourt, M.J.: Stable evaluation of Gaussian radial basis function interpolants. SIAM J. Sci. Comput. 34(2), A737\u2013A762 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"13_CR19","doi-asserted-by":"crossref","unstructured":"Fasshauer, G.E.: Meshfree approximation methods with MATLAB, Interdisciplinary Mathematical Sciences, vol. 6. World Scientific Publishing Co., Pte. Ltd., Hackensack, NJ: With 1 CD-ROM. (Windows, Macintosh and UNIX) (2007)","DOI":"10.1142\/6437"},{"issue":"1","key":"13_CR20","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1002\/zamm.19830630105","volume":"63","author":"JP Fink","year":"1983","unstructured":"Fink, J.P., Rheinboldt, W.C.: On the error behavior of the reduced basis technique for nonlinear finite element approximations. Z. Angew. Math. Mech. 63(1), 21\u201328 (1983)","journal-title":"Z. Angew. Math. Mech."},{"issue":"2","key":"13_CR21","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1137\/09076756X","volume":"33","author":"B Fornberg","year":"2011","unstructured":"Fornberg, B., Larsson, E., Flyer, N.: Stable computations with Gaussian radial basis functions. SIAM J. Sci. Comput. 33(2), 869\u2013892 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"13_CR22","doi-asserted-by":"crossref","first-page":"2270","DOI":"10.1016\/j.jcp.2010.12.014","volume":"230","author":"B Fornberg","year":"2011","unstructured":"Fornberg, B., Lehto, E.: Stabilization of RBF-generated finite difference methods for convective PDEs. J. Comput. Phys. 230(6), 2270\u20132285 (2011)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"13_CR23","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/j.camwa.2012.11.006","volume":"65","author":"B Fornberg","year":"2013","unstructured":"Fornberg, B., Lehto, E., Powell, C.: Stable calculation of Gaussian-based RBF-FD stencils. Comput. Math. Appl. 65(4), 627\u2013637 (2013)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"13_CR24","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1137\/060671991","volume":"30","author":"B Fornberg","year":"2008","unstructured":"Fornberg, B., Piret, C.: A stable algorithm for flat radial basis functions on a sphere. SIAM J. Sci. Comput. 30(1), 60\u201380 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5\u20136","key":"13_CR25","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1016\/j.camwa.2003.08.010","volume":"48","author":"B Fornberg","year":"2004","unstructured":"Fornberg, B., Wright, G.: Stable computation of multiquadric interpolants for all values of the shape parameter. Comput. Math. Appl. 48(5\u20136), 853\u2013867 (2004)","journal-title":"Comput. Math. Appl."},{"key":"13_CR26","first-page":"146","volume":"38","author":"P Gonnet","year":"2011","unstructured":"Gonnet, P., Pach\u00f3n, R., Trefethen, L.N.: Robust rational interpolation and least-squares. Electron. Trans. Numer. Anal. 38, 146\u2013167 (2011)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"3","key":"13_CR27","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1051\/m2an:2007031","volume":"41","author":"MA Grepl","year":"2007","unstructured":"Grepl, M.A., Maday, Y., Nguyen, N.C., Patera, A.T.: Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Math. Modell. Numer. Anal. 41(3), 575\u2013605 (2007)","journal-title":"Math. Modell. Numer. Anal."},{"issue":"1","key":"13_CR28","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1051\/m2an:2005006","volume":"39","author":"MA Grepl","year":"2005","unstructured":"Grepl, M.A., Patera, A.T.: A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Math. Model. Numer. Anal. 39(1), 157\u2013181 (2005)","journal-title":"Math. Model. Numer. Anal."},{"issue":"2","key":"13_CR29","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1051\/m2an:2008001","volume":"42","author":"B Haasdonk","year":"2008","unstructured":"Haasdonk, B., Ohlberger, M.: Reduced basis method for finite volume approximations of parametrized linear evolution equations. Math. Model. Numer. Anal. 42(2), 277\u2013302 (2008)","journal-title":"Math. Model. Numer. Anal."},{"key":"13_CR30","volume-title":"Spectral Methods for Time-Dependent Problems, Cambridge Monographs on Applied and Computational Mathematics","author":"JS Hesthaven","year":"2007","unstructured":"Hesthaven, J.S., Gottlieb, S., Gottlieb, D.: Spectral Methods for Time-Dependent Problems, Cambridge Monographs on Applied and Computational Mathematics, vol. 21. Cambridge University Press, Cambridge (2007)"},{"key":"13_CR31","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1016\/j.cma.2010.02.011","volume":"199","author":"DBP Huynh","year":"2010","unstructured":"Huynh, D.B.P., Knezevic, D.J., Chen, Y., Hesthaven, J.S., Patera, A.T.: A natural-norm successive constraint method for inf-sup lower bounds. Comput. Methods Appl. Mech. Eng. 199, 1963\u20131975 (2010)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"13_CR32","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/j.crma.2007.09.019","volume":"345","author":"DBP Huynh","year":"2007","unstructured":"Huynh, D.B.P., Rozza, G., Sen, S., Patera, A.T.: A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C. R. Acad. Sci. Paris S\u00e9r I. 345, 473\u2013478 (2007)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r I."},{"issue":"8\/9","key":"13_CR33","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0898-1221(90)90270-T","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa, E.J.: Multiquadrics\u2014a scattered data approximation scheme with applications to computational fluid dynamics I: surface approximations and partial derivative estimates. Comput. Math. Appl. 19(8\/9), 127\u2013145 (1990)","journal-title":"Comput. Math. Appl."},{"issue":"8\/9","key":"13_CR34","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa, E.J.: Multiquadrics\u2014a scattered data approximation scheme with applications to computational fluid dynamics II: solutions to parabolic, hyperbolic, and elliptic partial differential equations. Comput. Math. Appl. 19(8\/9), 147\u2013161 (1990)","journal-title":"Comput. Math. Appl."},{"issue":"5\u20136","key":"13_CR35","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/S0898-1221(03)90151-9","volume":"46","author":"E Larsson","year":"2003","unstructured":"Larsson, E., Fornberg, B.: A numerical study of some radial basis function based solution methods for elliptic PDEs. Comput. Math. Appl. 46(5\u20136), 891\u2013902 (2003)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"13_CR36","doi-asserted-by":"crossref","first-page":"A2096","DOI":"10.1137\/120899108","volume":"35","author":"E Larsson","year":"2013","unstructured":"Larsson, E., Lehto, E., Heryudono, A., Fornberg, B.: Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions. SIAM J. Sci. Comput. 35(4), A2096\u2013A2119 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"13_CR37","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1023\/A:1015145924517","volume":"17","author":"Y Maday","year":"2002","unstructured":"Maday, Y., Patera, A.T., Turinici, G.: A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. J. Sci. Comput. 17, 437\u2013446 (2002)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"13_CR38","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10444-004-1829-1","volume":"23","author":"SD Marchi","year":"2005","unstructured":"Marchi, S.D., Schaback, R., Wendland, H.: Near-optimal data-independent point locations for radial basis function interpolation. Adv. Comput. Math. 23(3), 317\u2013330 (2005)","journal-title":"Adv. Comput. Math."},{"issue":"2","key":"13_CR39","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/PL00005409","volume":"86","author":"AM Matache","year":"2000","unstructured":"Matache, A.M., Babu\u0161ka, I., Schwab, C.: Generalized $$p$$ p -FEM in homogenization. Numer. Math. 86(2), 319\u2013375 (2000)","journal-title":"Numer. Math."},{"key":"13_CR40","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01893414","volume":"2","author":"C Micchelli","year":"1986","unstructured":"Micchelli, C.: Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx. 2, 11\u201322 (1986)","journal-title":"Constr. Approx."},{"key":"13_CR41","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/0045-7949(79)90012-9","volume":"10","author":"DA Nagy","year":"1979","unstructured":"Nagy, D.A.: Modal representation of geometrically nonlinear behaviour by the finite element method. Comput. Struct. 10, 683\u2013688 (1979)","journal-title":"Comput. Struct."},{"key":"13_CR42","volume-title":"Large-Scale Inverse Problems and Quantification of Uncertainty","author":"NC Nguyen","year":"2010","unstructured":"Nguyen, N.C., Rozza, G., Huynh, D.B.P., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for parametrized parabolic pdes; application to real-time bayesian parameter estimation. In: Biegler, L., Biros, G., Ghattas, O., Heinkenschloss, M., Keyes, D., Mallick, B., Marzouk, Y., Tenorio, L., van Bloemen Waanders, B., Willcox, K. (eds.) Large-Scale Inverse Problems and Quantification of Uncertainty. Wiley, New York (2010)"},{"issue":"4","key":"13_CR43","doi-asserted-by":"crossref","first-page":"455","DOI":"10.2514\/3.50778","volume":"18","author":"AK Noor","year":"1980","unstructured":"Noor, A.K., Peters, J.M.: Reduced basis technique for nonlinear analysis of structures. AIAA J. 18(4), 455\u2013462 (1980)","journal-title":"AIAA J."},{"issue":"4","key":"13_CR44","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1137\/0910047","volume":"10","author":"JS Peterson","year":"1989","unstructured":"Peterson, J.S.: The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10(4), 777\u2013786 (1989)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"2","key":"13_CR45","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1137\/090774707","volume":"53","author":"RB Platte","year":"2011","unstructured":"Platte, R.B., Trefethen, L.N., Kuijlaars, A.B.J.: Impossibility of fast stable approximation of analytic functions from equispaced samples. SIAM Rev. 53(2), 308\u2013318 (2011)","journal-title":"SIAM Rev."},{"issue":"4","key":"13_CR46","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1093\/imanum\/drq020","volume":"31","author":"RB Platte","year":"2011","unstructured":"Platte, R.B.: How fast do radial basis function interpolants of analytic functions converge? IMA J. Numer. Anal. 31(4), 1578\u20131597 (2011)","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"13_CR47","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1137\/040610143","volume":"43","author":"RB Platte","year":"2005","unstructured":"Platte, R.B., Driscoll, T.A.: Polynomials and potential theory for Gaussian radial basis function interpolation. SIAM J. Numer. Anal. 43(2), 750\u2013766 (2005). (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"172","key":"13_CR48","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1090\/S0025-5718-1985-0804937-0","volume":"45","author":"TA Porsching","year":"1985","unstructured":"Porsching, T.A.: Estimation of the error in the reduced basis method solution of nonlinear equations. Math. Comput. 45(172), 487\u2013496 (1985)","journal-title":"Math. Comput."},{"issue":"1","key":"13_CR49","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1115\/1.1448332","volume":"124","author":"C Prud\u2019homme","year":"2002","unstructured":"Prud\u2019homme, C., Rovas, D., Veroy, K., Maday, Y., Patera, A.T., Turinici, G.: Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J. Fluids Eng. 124(1), 70\u201380 (2002)","journal-title":"J. Fluids Eng."},{"issue":"3","key":"13_CR50","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11831-008-9019-9","volume":"15","author":"G Rozza","year":"2008","unstructured":"Rozza, G., Huynh, D.B.P., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: application to transport and continuum mechanics. Arch. Comput. Methods Eng. 15(3), 229\u2013275 (2008)","journal-title":"Arch. Comput. Methods Eng."},{"key":"13_CR51","volume-title":"Spectral and High-Order Methods with Applications, Mathematics Monograph Series","author":"J Shen","year":"2006","unstructured":"Shen, J., Tang, T.: Spectral and High-Order Methods with Applications, Mathematics Monograph Series, vol. 3. Science Press Beijing, Beijing (2006)"},{"issue":"2","key":"13_CR52","first-page":"195","volume":"7","author":"C Shu","year":"2005","unstructured":"Shu, C., Ding, H., Yeo, K.S.: Computation of incompressible Navier\u2013Stokes equations by local RBF-based differential quadrature method. CMES Comput. Model. Eng. Sci. 7(2), 195\u2013205 (2005)","journal-title":"CMES Comput. Model. Eng. Sci."},{"issue":"1","key":"13_CR53","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s00466-003-0501-9","volume":"33","author":"AI Tolstykh","year":"2003","unstructured":"Tolstykh, A.I., Shirobokov, D.A.: On using radial basis functions in a \u201cfinite difference mode\u201d with applications to elasticity problems. Comput. Mech. 33(1), 68\u201379 (2003)","journal-title":"Comput. Mech."},{"key":"13_CR54","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719598","volume-title":"Spectral Methods in MATLAB, Software, Environments, and Tools","author":"LN Trefethen","year":"2000","unstructured":"Trefethen, L.N.: Spectral Methods in MATLAB, Software, Environments, and Tools, vol. 10. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2000)"},{"issue":"288","key":"13_CR55","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.1090\/S0025-5718-2013-02782-2","volume":"83","author":"K Urban","year":"2014","unstructured":"Urban, K., Patera, A.T.: An improved error bound for reduced basis approximation of linear parabolic problems. Math. Comput. 83(288), 1599\u20131615 (2014)","journal-title":"Math. Comput."},{"issue":"9","key":"13_CR56","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.crma.2003.09.023","volume":"337","author":"K Veroy","year":"2003","unstructured":"Veroy, K., Prud\u2019homme, C., Patera, A.T.: Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds. C. R. Acad. Sci. Paris S\u00e9r I 337(9), 619\u2013624 (2003)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r I"},{"issue":"4","key":"13_CR57","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF02123482","volume":"4","author":"H Wendland","year":"1995","unstructured":"Wendland, H.: Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math. 4(4), 389\u2013396 (1995)","journal-title":"Adv. Comput. Math."},{"key":"13_CR58","volume-title":"Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics","author":"H Wendland","year":"2005","unstructured":"Wendland, H.: Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, vol. 17. Cambridge University Press, Cambridge (2005)"},{"issue":"1","key":"13_CR59","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.jcp.2005.05.030","volume":"212","author":"GB Wright","year":"2006","unstructured":"Wright, G.B., Fornberg, B.: Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comput. Phys. 212(1), 99\u2013123 (2006)","journal-title":"J. Comput. Phys."},{"issue":"2155","key":"13_CR60","doi-asserted-by":"crossref","first-page":"20130036","DOI":"10.1098\/rspa.2013.0036","volume":"469","author":"M Yano","year":"2013","unstructured":"Yano, M., Patera, A.T.: A space\u2013time variational approach to hydrodynamic stability theory. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469(2155), 20130036 (2013)","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"issue":"9","key":"13_CR61","doi-asserted-by":"crossref","first-page":"1903","DOI":"10.1142\/S0218202514500110","volume":"24","author":"M Yano","year":"2014","unstructured":"Yano, M., Patera, Anthony T., Urban, K.: A space\u2013time $$hp$$ h p -interpolation-based certified reduced basis method for Burgers\u2019 equation. Math. Models Methods Appl. Sci. 24(9), 1903\u20131935 (2014)","journal-title":"Math. Models Methods Appl. Sci."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0013-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-015-0013-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0013-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T09:44:35Z","timestamp":1566467075000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-015-0013-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,25]]},"references-count":61,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["13"],"URL":"https:\/\/doi.org\/10.1007\/s10915-015-0013-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,25]]}}}