Convergence of finite elements on an evolving surface driven by diffusion on the surface

[1]  R. Nürnberg,et al.  Erratum: Numerical computations of the dynamics of fluidic membranes and vesicles [Phys. Rev. E 92, 052704 (2015)]. , 2016, Physical Review E.

[2]  John W. Barrett,et al.  Numerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the Curve , 2016, SIAM J. Numer. Anal..

[3]  Balázs Kovács,et al.  High-order evolving surface finite element method for parabolic problems on evolving surfaces , 2016, 1606.07234.

[4]  Harald Garcke,et al.  A stable numerical method for the dynamics of fluidic membranes , 2016, Numerische Mathematik.

[5]  Paola Pozzi,et al.  Curve shortening flow coupled to lateral diffusion , 2015, Numerische Mathematik.

[6]  Bal'azs Kov'acs,et al.  Maximum norm stability and error estimates for the evolving surface finite element method , 2015, 1510.00605.

[7]  Harald Garcke,et al.  Numerical computations of the dynamics of fluidic membranes and vesicles. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Bal'azs Kov'acs,et al.  Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces , 2015, 1503.08990.

[9]  Bal'azs Kov'acs,et al.  Higher-order time discretizations with ALE finite elements for parabolic problems on evolving surfaces , 2014, 1410.0486.

[10]  C. M. Elliott,et al.  Error analysis for an ALE evolving surface finite element method , 2014, 1403.1402.

[11]  Chandrasekhar Venkataraman,et al.  Backward difference time discretization of parabolic differential equations on evolving surfaces , 2013 .

[12]  Harald Garcke,et al.  A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow , 2013, Journal of Scientific Computing.

[13]  Gerhard Dziuk,et al.  Scalar conservation laws on moving hypersurfaces , 2013, 1307.1056.

[14]  Charles M. Elliott,et al.  Finite element methods for surface PDEs* , 2013, Acta Numerica.

[15]  C. M. Elliott,et al.  An ALE ESFEM for Solving PDEs on Evolving Surfaces , 2012 .

[16]  C. M. Elliott,et al.  A Fully Discrete Evolving Surface Finite Element Method , 2012, SIAM J. Numer. Anal..

[17]  Charles M. Elliott,et al.  L2-estimates for the evolving surface finite element method , 2012, Math. Comput..

[18]  Gerhard Dziuk,et al.  Runge–Kutta time discretization of parabolic differential equations on evolving surfaces , 2012 .

[19]  C. M. Elliott,et al.  The surface finite element method for pattern formation on evolving biological surfaces , 2011, Journal of mathematical biology.

[20]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[21]  Alan Demlow,et al.  Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces , 2009, SIAM J. Numer. Anal..

[22]  Charles M. Elliott,et al.  Finite elements on evolving surfaces , 2007 .

[23]  Charles M. Elliott,et al.  A free-boundary model for diffusion-induced grain boundary motion , 2001 .

[24]  I. Graham,et al.  Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth , 2001, Journal of mathematical biology.

[25]  G. Dziuk,et al.  An algorithm for evolutionary surfaces , 1990 .

[26]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[27]  Paola Pozzi,et al.  Curve shortening ow coupled to lateral diusion , 2015 .

[28]  G. Dziuk.  Finite Elements for the Beltrami operator on arbitrary surfaces , 1988 .