Finite element analysis for a diffusion equation on a harmonically evolving domain

DOI10.1093/IMANUM/DRAB026zbMATH Open1501.65069arXiv2009.11105OpenAlexW3160760109MaRDI QIDQ5075171

Dominik Edelmann

Publication date: 10 May 2022

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Abstract: We study convergence of the evolving finite element semi-discretization of a parabolic partial differential equation on an evolving bulk domain. The boundary of the domain evolves with a given velocity, which is then extended to the bulk by solving a Poisson equation. The numerical solution to the parabolic equation depends on the numerical evolution of the bulk, which yields the time-dependent mesh for the finite element method. The stability analysis works with the matrix-vector formulation of the semi-discretization only and does not require geometric arguments, which are then required in the proof of consistency estimates. We present various numerical experiments that illustrate the proven convergence rates.

Full work available at URL: https://arxiv.org/abs/2009.11105

zbMATH Keywords

diffusionerror analysisevolving finite elementsevolving domainharmonic velocity

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Higher-order parabolic equations (35K25)

Related Items (1)

A convergent evolving finite element method with artificial tangential motion for surface evolution under a prescribed velocity field

This page was built for publication: Finite element analysis for a diffusion equation on a harmonically evolving domain

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5075171)