Variational discretization of wave equations on evolving surfaces

DOI10.1090/S0025-5718-2014-02882-2zbMath1307.65136MaRDI QIDQ5496204

Christian Lubich, Dhia Mansour

Publication date: 30 January 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergencewave equationerror analysisCourant-Friedrichs-Lewy conditionnumerical experimentStörmer-Verlet methodvariational integratorleapfrog methodRitz projectionevolving surface finite element method

Mathematics Subject Classification ID

Wave equation (35L05) 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) Hyperbolic equations on manifolds (58J45)

Related Items

Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces ⋮ A finite area scheme for shallow granular flows on three-dimensional surfaces ⋮ Lumped finite elements for reaction-cross-diffusion systems on stationary surfaces ⋮ Evolving Surface Finite Element Methods for Random Advection-Diffusion Equations ⋮ A fully Lagrangian meshfree framework for PDEs on evolving surfaces ⋮ A convergent algorithm for forced mean curvature flow driven by diffusion on the surface ⋮ Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces ⋮ Gauss-Runge-Kutta time discretization of wave equations on evolving surfaces ⋮ A Convergent evolving finite element algorithm for Willmore flow of closed surfaces ⋮ Error analysis for an ALE evolving surface finite element method

Uses Software

• DUNE-FEM
• RODAS

Cites Work

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