Li, Buyang Convergence of Dziuk’s linearly implicit parametric finite element method for curve shortening flow. (English) Zbl 1452.65240 SIAM J. Numer. Anal. 58, No. 4, 2315-2333 (2020). MSC: 65M60 65M15 35K55 35K65 65M22 PDF BibTeX XML Cite \textit{B. Li}, SIAM J. Numer. Anal. 58, No. 4, 2315--2333 (2020; Zbl 1452.65240) Full Text: DOI
Kovács, Balázs; Li, Buyang; Lubich, Christian A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. (English) Zbl 1427.65250 Numer. Math. 143, No. 4, 797-853 (2019). MSC: 65M60 65M15 65M12 35R01 PDF BibTeX XML Cite \textit{B. Kovács} et al., Numer. Math. 143, No. 4, 797--853 (2019; Zbl 1427.65250) Full Text: DOI arXiv
Dörfler, Willy; Nürnberg, Robert Discrete gradient flows for General curvature energies. (English) Zbl 1434.65178 SIAM J. Sci. Comput. 41, No. 3, A2012-A2036 (2019). Reviewer: Song Jiang (Beijing) MSC: 65M60 65M12 35K55 74E10 53C99 PDF BibTeX XML Cite \textit{W. Dörfler} and \textit{R. Nürnberg}, SIAM J. Sci. Comput. 41, No. 3, A2012--A2036 (2019; Zbl 1434.65178) Full Text: DOI
Barrett, John W.; Garcke, Harald; Nürnberg, Robert Variational discretization of axisymmetric curvature flows. (English) Zbl 1419.65051 Numer. Math. 141, No. 3, 791-837 (2019). Reviewer: Dana Černá (Liberec) MSC: 65M60 65M12 53C44 35K55 65H10 PDF BibTeX XML Cite \textit{J. W. Barrett} et al., Numer. Math. 141, No. 3, 791--837 (2019; Zbl 1419.65051) Full Text: DOI
Glickenstein, David; Liang, Jinjin Asymptotic behavior of \(\beta \)-polygon flows. (English) Zbl 1407.53064 J. Geom. Anal. 28, No. 3, 2902-2925 (2018). MSC: 53C44 58E50 51E12 PDF BibTeX XML Cite \textit{D. Glickenstein} and \textit{J. Liang}, J. Geom. Anal. 28, No. 3, 2902--2925 (2018; Zbl 1407.53064) Full Text: DOI arXiv
Kröner, Axel; Kröner, Eva; Kröner, Heiko Finite element approximation of level set motion by powers of the mean curvature. (English) Zbl 1404.35215 SIAM J. Sci. Comput. 40, No. 6, A4158-A4183 (2018). MSC: 35J93 65L60 35D40 PDF BibTeX XML Cite \textit{A. Kröner} et al., SIAM J. Sci. Comput. 40, No. 6, A4158--A4183 (2018; Zbl 1404.35215) Full Text: DOI
Barrett, John W.; Deckelnick, Klaus; Styles, Vanessa Numerical analysis for a system coupling curve evolution to reaction diffusion on the curve. (English) Zbl 1365.65218 SIAM J. Numer. Anal. 55, No. 2, 1080-1100 (2017). MSC: 65M60 65M15 35K55 53C44 74N20 74S05 35K57 PDF BibTeX XML Cite \textit{J. W. Barrett} et al., SIAM J. Numer. Anal. 55, No. 2, 1080--1100 (2017; Zbl 1365.65218) Full Text: DOI arXiv
Pozzi, Paola; Stinner, Björn Curve shortening flow coupled to lateral diffusion. (English) Zbl 1369.65111 Numer. Math. 135, No. 4, 1171-1205 (2017). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M20 65M15 65M60 35K40 65M12 PDF BibTeX XML Cite \textit{P. Pozzi} and \textit{B. Stinner}, Numer. Math. 135, No. 4, 1171--1205 (2017; Zbl 1369.65111) Full Text: DOI arXiv
Perl, Ricardo; Pozzi, Paola; Rumpf, Martin A nested variational time discretization for parametric anisotropic Willmore flow. (English) Zbl 1325.49033 Griebel, Michael (ed.), Singular phenomena and scaling in mathematical models. Cham: Springer (ISBN 978-3-319-00785-4/hbk; 978-3-319-00786-1/ebook). 221-241 (2014). MSC: 49M25 49M15 49Q10 49Q20 PDF BibTeX XML Cite \textit{R. Perl} et al., in: Singular phenomena and scaling in mathematical models. Cham: Springer. 221--241 (2014; Zbl 1325.49033) Full Text: DOI arXiv
Mikula, Karol; Urbán, Jozef A new tangentially stabilized 3D curve evolution algorithm and its application in virtual colonoscopy. (English) Zbl 1296.65030 Adv. Comput. Math. 40, No. 4, 819-837 (2014). MSC: 65D17 92C55 35R01 65M08 68U10 PDF BibTeX XML Cite \textit{K. Mikula} and \textit{J. Urbán}, Adv. Comput. Math. 40, No. 4, 819--837 (2014; Zbl 1296.65030) Full Text: DOI
Ševčovič, Daniel; Yazaki, Shigetoshi Computational and qualitative aspects of motion of plane curves with a curvature adjusted tangential velocity. (English) Zbl 1255.35148 Math. Methods Appl. Sci. 35, No. 15, 1784-1798 (2012). MSC: 35K65 65N40 53C80 PDF BibTeX XML Cite \textit{D. Ševčovič} and \textit{S. Yazaki}, Math. Methods Appl. Sci. 35, No. 15, 1784--1798 (2012; Zbl 1255.35148) Full Text: DOI
Ševčovič, Daniel; Yazaki, Shigetoshi Evolution of plane curves with a curvature adjusted tangential velocity. (English) Zbl 1291.35109 Japan J. Ind. Appl. Math. 28, No. 3, 413-442 (2011). MSC: 35K40 35K55 65N08 PDF BibTeX XML Cite \textit{D. Ševčovič} and \textit{S. Yazaki}, Japan J. Ind. Appl. Math. 28, No. 3, 413--442 (2011; Zbl 1291.35109) Full Text: DOI arXiv
Barrett, John W.; Garcke, Harald; Nürnberg, Robert The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute. (English) Zbl 1218.65105 Numer. Methods Partial Differ. Equations 27, No. 1, 1-30 (2011). Reviewer: Juan Monterde (Burjasot) MSC: 65M60 65M50 65M12 35K55 PDF BibTeX XML Cite \textit{J. W. Barrett} et al., Numer. Methods Partial Differ. Equations 27, No. 1, 1--30 (2011; Zbl 1218.65105) Full Text: DOI
Barrett, John W.; Garcke, Harald; Nürnberg, Robert Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering. (English) Zbl 1410.80015 Eur. J. Appl. Math. 21, No. 6, 519-556 (2010). MSC: 80M10 65N12 65N30 PDF BibTeX XML Cite \textit{J. W. Barrett} et al., Eur. J. Appl. Math. 21, No. 6, 519--556 (2010; Zbl 1410.80015) Full Text: DOI
Handlovičová, Angela; Mikula, Karol Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. (English) Zbl 1199.35197 Appl. Math., Praha 53, No. 2, 105-129 (2008). MSC: 35K93 65M12 65M08 PDF BibTeX XML Cite \textit{A. Handlovičová} and \textit{K. Mikula}, Appl. Math., Praha 53, No. 2, 105--129 (2008; Zbl 1199.35197) Full Text: DOI EuDML
Barrett, John W.; Garcke, Harald; Nürnberg, Robert On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\). (English) Zbl 1145.65068 J. Comput. Phys. 227, No. 9, 4281-4307 (2008). Reviewer: Marius Ghergu (Slatina) MSC: 65M60 65M12 35K55 53C44 PDF BibTeX XML Cite \textit{J. W. Barrett} et al., J. Comput. Phys. 227, No. 9, 4281--4307 (2008; Zbl 1145.65068) Full Text: DOI
Yazaki, Shigetoshi On the tangential velocity arising in a crystallinge approximation of evolving plane curves. (English) Zbl 1139.53033 Kybernetika 43, No. 6, 913-918 (2007). MSC: 53C44 34A26 34A34 35K65 53A04 53C80 65L20 65M12 65N12 PDF BibTeX XML Cite \textit{S. Yazaki}, Kybernetika 43, No. 6, 913--918 (2007; Zbl 1139.53033) Full Text: Link EuDML
Carlini, E.; Falcone, M.; Ferretti, R. A semi-Lagrangian scheme for the curve shortening flow in codimension-2. (English) Zbl 1255.65157 J. Comput. Phys. 225, No. 2, 1388-1408 (2007). MSC: 65M06 60H35 74K10 PDF BibTeX XML Cite \textit{E. Carlini} et al., J. Comput. Phys. 225, No. 2, 1388--1408 (2007; Zbl 1255.65157) Full Text: DOI
Mikula, Karol; Ševčovič, Daniel Evolution of curves on a surface driven by the geodesic curvature and external force. (English) Zbl 1097.35084 Appl. Anal. 85, No. 4, 345-362 (2006). Reviewer: Christine Guenther (Forest Grove) MSC: 35K65 35B35 35K55 53C44 35K50 PDF BibTeX XML Cite \textit{K. Mikula} and \textit{D. Ševčovič}, Appl. Anal. 85, No. 4, 345--362 (2006; Zbl 1097.35084) Full Text: DOI
Elliott, C. M.; Styles, V. Computations of bidirectional grain boundary dynamics in thin metallic films. (English) Zbl 1020.82006 J. Comput. Phys. 187, No. 2, 524-543 (2003). MSC: 82C26 PDF BibTeX XML Cite \textit{C. M. Elliott} and \textit{V. Styles}, J. Comput. Phys. 187, No. 2, 524--543 (2003; Zbl 1020.82006) Full Text: DOI
Richardson, G. Instability of a superconducting line vortex. (English) Zbl 0925.82220 Physica D 110, No. 1-2, 139-153 (1997). MSC: 82D55 PDF BibTeX XML Cite \textit{G. Richardson}, Physica D 110, No. 1--2, 139--153 (1997; Zbl 0925.82220) Full Text: DOI
Kimura, Masato Numerical analysis of moving boundary problems using the boundary tracking method. (English) Zbl 0892.76065 Japan J. Ind. Appl. Math. 14, No. 3, 373-398 (1997). MSC: 76M25 76D99 PDF BibTeX XML Cite \textit{M. Kimura}, Japan J. Ind. Appl. Math. 14, No. 3, 373--398 (1997; Zbl 0892.76065) Full Text: DOI
Mikula, Karol Solution of nonlinear curvature driven evolution of plane convex curves. (English) Zbl 0877.65068 Appl. Numer. Math. 23, No. 3, 347-360 (1997). Reviewer: S.Jiang (Beijing) MSC: 65M20 35K55 65M12 PDF BibTeX XML Cite \textit{K. Mikula}, Appl. Numer. Math. 23, No. 3, 347--360 (1997; Zbl 0877.65068) Full Text: DOI