Error analysis for an ALE evolving surface finite element method

DOI10.1002/num.21930zbMath1318.65063arXiv1403.1402OpenAlexW1864128760WikidataQ58871736 ScholiaQ58871736MaRDI QIDQ5246764

Charles M. Elliott, Chandrasekhar Venkataraman

Publication date: 22 April 2015

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.1402

zbMATH Keywords

convergencefinite elementserror analysisnumerical experimentevolving surfaceslinear advection-diffusion equationarbitrary Lagrange-Euler method

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (12)

Numerical modeling of phase separation on dynamic surfaces ⋮ Numerical preservation of velocity induced invariant regions for reaction-diffusion systems on evolving surfaces ⋮ Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces ⋮ Unified Analysis of Finite Element Methods for Problems with Moving Boundaries ⋮ Convergence of finite elements on an evolving surface driven by diffusion on the surface ⋮ A Trace Finite Element Method for PDEs on Evolving Surfaces ⋮ Stabilized finite element approximation of the Swift-Hohenberg model on evolving surfaces ⋮ A convergent algorithm for forced mean curvature flow driven by diffusion on the surface ⋮ Mini-workshop: PDE models of motility and invasion in active biosystems. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ On algorithms with good mesh properties for problems with moving boundaries based on the Harmonic Map Heat Flow and the DeTurck trick ⋮ Fluid deformable surfaces ⋮ Time-Periodic Solutions of Advection-Diffusion Equations on Moving Hypersurfaces

Uses Software

• ALBERTA
• ParaView

Cites Work

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• $L^2$-estimates for the evolving surface finite element method
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• Variational discretization of wave equations on evolving surfaces

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