{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T18:10:15Z","timestamp":1738260615243,"version":"3.35.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2008,6,1]],"date-time":"2008-06-01T00:00:00Z","timestamp":1212278400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2008,6]]},"DOI":"10.1007\/s10915-008-9204-x","type":"journal-article","created":{"date-parts":[[2008,6,12]],"date-time":"2008-06-12T20:10:09Z","timestamp":1213301409000},"page":"77-98","source":"Crossref","is-referenced-by-count":6,"title":["Finite Element-Based Level Set Methods for Higher Order Flows"],"prefix":"10.1007","volume":"35","author":[{"given":"Martin","family":"Burger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christina","family":"St\u00f6cker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Axel","family":"Voigt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,6,13]]},"reference":[{"key":"9204_CR1","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1142\/S0218348X95000631","volume":"3","author":"F. Almgren","year":"1996","unstructured":"Almgren, F., Taylor, J.E.: Optimal geometry in equilibrium and growth. Fractals 3, 713\u2013723 (1996)","journal-title":"Fractals"},{"key":"9204_CR2","volume-title":"Metric Gradient Flows","author":"L. Ambrosio","year":"2005","unstructured":"Ambrosio, L., Gigli, N., Savare, G.: Metric Gradient Flows. Birkh\u00e4user, Basel (2005)"},{"unstructured":"www.caesar.de\/amdis.html","key":"9204_CR3"},{"key":"9204_CR4","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.jcp.2004.08.022","volume":"203","author":"E. B\u00e4nsch","year":"2005","unstructured":"B\u00e4nsch, E., Morin, P., Nochetto, R.H.: A finite element method for surface diffusion: the parametric case. J. Comput. Phys. 203, 321\u2013343 (2005)","journal-title":"J. Comput. Phys."},{"key":"9204_CR5","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1090\/S0025-5718-99-01015-7","volume":"68","author":"J.W. Barrett","year":"1999","unstructured":"Barrett, J.W., Blowey, J.F.: Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility. Math. Comp. 68, 487\u2013517 (1999)","journal-title":"Math. Comp."},{"key":"9204_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods","author":"F. Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991)"},{"key":"9204_CR7","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s00791-006-0016-y","volume":"9","author":"F. Bornemann","year":"2006","unstructured":"Bornemann, F., Rasch, C.: Finite-Element discretization of static Hamilton-Jacobi equations based on a local variational principle. Comput. Vis. Sci. 9, 57\u201369 (2006)","journal-title":"Comput. Vis. Sci."},{"key":"9204_CR8","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/j.jcp.2004.08.024","volume":"203","author":"M. Burger","year":"2005","unstructured":"Burger, M.: Numerical simulation of anisotropic surface diffusion with curvature-dependent energy. J. Comp. Phys. 203, 602\u2013625 (2005)","journal-title":"J. Comp. Phys."},{"key":"9204_CR9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.jcp.2006.11.026","volume":"225","author":"M. Burger","year":"2007","unstructured":"Burger, M., Hausser, F., St\u00f6cker, C., Voigt, A.: A level set approach to anisotropic flows with curvature regularization. J. Comp. Phys. 225, 183\u2013205 (2007)","journal-title":"J. Comp. Phys."},{"issue":"12","key":"9204_CR10","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1007\/s11837-997-0027-2","volume":"49","author":"W.C. Carter","year":"1998","unstructured":"Carter, W.C., Cahn, J.W., Taylor, J.E.: Variational methods for microstructural evolution. JOM 49(12), 30\u201336 (1998)","journal-title":"JOM"},{"key":"9204_CR11","doi-asserted-by":"crossref","first-page":"195","DOI":"10.4171\/IFB\/97","volume":"6","author":"A. Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for mean curvature motion. Interfaces Free Bound. 6, 195\u2013218 (2004)","journal-title":"Interfaces Free Bound."},{"key":"9204_CR12","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/3-7643-7343-1_14","volume-title":"Multiscale Modeling in Epitaxial Growth, ISNM 149","author":"U. Clarenz","year":"2005","unstructured":"Clarenz, U., Hau\u00dfer, F., Rumpf, M., Voigt, A., Weikard, U.: On level set formulations for anisotropic fourth order geometric evolution problems. In: Voigt, A. (ed.) Multiscale Modeling in Epitaxial Growth, ISNM 149, pp. 227\u2013237. Birkh\u00e4user, Basel (2005)"},{"key":"9204_CR13","doi-asserted-by":"crossref","first-page":"341","DOI":"10.4171\/IFB\/24","volume":"2","author":"K. Deckelnick","year":"2000","unstructured":"Deckelnick, K., Dziuk, G.: Error estimates for a semi implicit fully discrete finite element scheme for mean curvature flow of graphs. Interfaces Free Bound. 2, 341\u2013359 (2000)","journal-title":"Interfaces Free Bound."},{"key":"9204_CR14","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s002110100322","volume":"91","author":"K. Deckelnick","year":"2002","unstructured":"Deckelnick, K., Dziuk, G.: A fully discrete numerical scheme for weighted mean curvature flow. Numer. Math. 91, 423\u2013452 (2002)","journal-title":"Numer. Math."},{"key":"9204_CR15","volume-title":"Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs","author":"K. Deckelnick","year":"2003","unstructured":"Deckelnick, K., Dziuk, G., Elliott, C.M.: Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs. Isaac Newton Institute, Cambridge (2003). Preprint"},{"doi-asserted-by":"crossref","unstructured":"Deckelnick, K., Dziuk, G., Elliott, C.M.: Computation of geometric partial differential equations and mean curvature flow. Acta Numer. (2005), 139\u2013232","key":"9204_CR16","DOI":"10.1017\/S0962492904000224"},{"key":"9204_CR17","volume-title":"Shapes and Geometries. Analysis, Differential Calculus, and Optimization","author":"M.C. Delfour","year":"2001","unstructured":"Delfour, M.C., Zol\u00e9sio, J.P.: Shapes and Geometries. Analysis, Differential Calculus, and Optimization. SIAM, Philadelphia (2001)"},{"key":"9204_CR18","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1137\/0152065","volume":"52","author":"A. DiCarlo","year":"1992","unstructured":"DiCarlo, A., Gurtin, M., Podio-Guidugli, P.: A regularized equation for anisotropic motion by curvature. SIAM J. Appl. Math. 52, 1111\u20131119 (1992)","journal-title":"SIAM J. Appl. Math."},{"key":"9204_CR19","doi-asserted-by":"crossref","first-page":"361","DOI":"10.4171\/IFB\/105","volume":"6","author":"M. Droske","year":"2004","unstructured":"Droske, M., Rumpf, M.: A level set formulation for Willmore flow. Interfaces Free Bound. 6, 361\u2013378 (2004)","journal-title":"Interfaces Free Bound."},{"key":"9204_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0065-2156(04)40001-5","volume":"40","author":"E. Fried","year":"2004","unstructured":"Fried, E., Gurtin, M.E.: A unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain-boundaries and epitaxy. Adv. Appl. Mech. 40, 1\u2013177 (2004)","journal-title":"Adv. Appl. Mech."},{"key":"9204_CR21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1088\/0951-7715\/16\/1\/304","volume":"16","author":"K. Glasner","year":"2003","unstructured":"Glasner, K.: A diffuse interface approach to Hele-Shaw flow. Nonlinearity 16, 49\u201366 (2003)","journal-title":"Nonlinearity"},{"key":"9204_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/ifb\/129","volume":"7","author":"F. Hau\u00dfer","year":"2005","unstructured":"Hau\u00dfer, F., Voigt, A.: A discrete scheme for regularized anisotropic surface diffusion, a sixth order geometric evolution equation. Interfaces Free Bound. 7, 1\u201317 (2005)","journal-title":"Interfaces Free Bound."},{"key":"9204_CR23","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/j.aml.2005.05.011","volume":"19","author":"F. Hau\u00dfer","year":"2006","unstructured":"Hau\u00dfer, F., Voigt, A.: A discrete scheme for regularized anisotropic curve shortening flow. Appl. Math. Lett. 19, 691\u2013698 (2006)","journal-title":"Appl. Math. Lett."},{"key":"9204_CR24","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10915-005-9064-6","volume":"30","author":"F. Hau\u00dfer","year":"2007","unstructured":"Hau\u00dfer, F., Voigt, A.: A discrete scheme for parametric anisotropic surface diffusion. J. Sci. Comput. 30, 223\u2013235 (2007)","journal-title":"J. Sci. Comput."},{"key":"9204_CR25","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1103\/PhysRev.82.87","volume":"82","author":"C. Herring","year":"1951","unstructured":"Herring, C.: Some theorems on the free energies of crystal surfaces. Phys. Rev. 82, 87\u201393 (1951)","journal-title":"Phys. Rev."},{"key":"9204_CR26","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s002050200193","volume":"163","author":"M.E. Gurtin","year":"2002","unstructured":"Gurtin, M.E., Jabbour, M.E.: Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films. Arch. Rat. Mech. Anal. 163, 171\u2013208 (2002)","journal-title":"Arch. Rat. Mech. Anal."},{"key":"9204_CR27","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1063\/1.1722742","volume":"28","author":"W.W. Mullins","year":"1957","unstructured":"Mullins, W.W.: Theory of thermal grooving. J. Appl. Phys. 28, 333\u2013339 (1957)","journal-title":"J. Appl. Phys."},{"key":"9204_CR28","volume-title":"The Level Set Method and Dynamic Implicit Surfaces","author":"S.J. Osher","year":"2002","unstructured":"Osher, S.J., Fedkiw, R.P.: The Level Set Method and Dynamic Implicit Surfaces. Springer, New York (2002)"},{"key":"9204_CR29","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S.J. Osher","year":"1988","unstructured":"Osher, S.J., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton\u2013Jacobi formulations. J. Comp. Phys. 79, 12\u201349 (1988)","journal-title":"J. Comp. Phys."},{"key":"9204_CR30","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1166\/jctn.2006.3041","volume":"3","author":"A. R\u00e4tz","year":"2006","unstructured":"R\u00e4tz, A., Voigt, A.: Higher order regularization of anisotropic geometric evolution equations in three dimensions. J. Comput. Theor. Nanosci. 3, 543\u2013560 (2006)","journal-title":"J. Comput. Theor. Nanosci."},{"key":"9204_CR31","doi-asserted-by":"crossref","first-page":"229","DOI":"10.4171\/IFB\/122","volume":"7","author":"R.E. Rusu","year":"2005","unstructured":"Rusu, R.E.: An algorithm for the elastic flow of surfaces. Interfaces Free Bound. 7, 229\u2013239 (2005)","journal-title":"Interfaces Free Bound."},{"key":"9204_CR32","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1023\/A:1025324613450","volume":"19","author":"P. Smereka","year":"2003","unstructured":"Smereka, P.: Semi-implicit level set methods for curvature and surface diffusion motion. J. Sci. Comp. 19, 439\u2013456 (2003)","journal-title":"J. Sci. Comp."},{"unstructured":"St\u00f6cker, C.: Level set methods for higher order evolution laws. PhD-thesis, Mathematics Department, Technische Universit\u00e4t Dresden (2008). http:\/\/nbn-resolving.de\/urn:nbn:de:bsz:14-ds-1205350171405-81971","key":"9204_CR33"},{"key":"9204_CR34","first-page":"111","volume":"4","author":"C. St\u00f6cker","year":"2005","unstructured":"St\u00f6cker, C., Vey, S., Voigt, A.: AMDiS\u2014Adaptive multidimensional simulations: composite finite elements and signed distance functions. WSEAS Trans. Circ. Syst. 4, 111\u2013116 (2005)","journal-title":"WSEAS Trans. Circ. Syst."},{"key":"9204_CR35","first-page":"1564","volume":"3","author":"S. Vey","year":"2004","unstructured":"Vey, S., Voigt, A.: AMDiS\u2014adaptive multidimensional simulations: Object oriented software concepts for scientific computing. WSEAS Trans. Syst. 3, 1564\u2013159 (2004)","journal-title":"WSEAS Trans. Syst."},{"key":"9204_CR36","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s00791-006-0048-3","volume":"10","author":"S. Vey","year":"2007","unstructured":"Vey, S., Voigt, A.: AMDiS\u2014adaptive multidimensional simulations. Comp. Vis. Sci. 10, 57\u201367 (2007)","journal-title":"Comp. Vis. Sci."},{"key":"9204_CR37","first-page":"813","volume":"81","author":"S. Vey","year":"2007","unstructured":"Vey, S., Voigt, A.: Adaptive full domain covering meshes for parallel finit element computations. Comput. 81, 813\u2013820 (2007)","journal-title":"Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-008-9204-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-008-9204-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-008-9204-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T17:54:58Z","timestamp":1738259698000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-008-9204-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":37,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["9204"],"URL":"https:\/\/doi.org\/10.1007\/s10915-008-9204-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}