A Priori Error Estimates for the Finite Element Approximation of Westervelt's Quasi-linear Acoustic Wave Equation

DOI10.1137/19M1240873zbMath1476.65247arXiv1901.08510OpenAlexW2966298938MaRDI QIDQ5232311

Vanja Nikolić, Barbara I. Wohlmuth

Publication date: 2 September 2019

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.08510

zbMATH Keywords

finite element methodnonlinear acousticsa priori analysisWestervelt's equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) A priori estimates in context of PDEs (35B45) Hydro- and aero-acoustics (76Q05) 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)

Related Items (8)

Numerical Upscaling for Wave Equations with Time-Dependent Multiscale Coefficients ⋮ Exponential Integrators for Quasilinear Wave-Type Equations ⋮ A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes ⋮ A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation ⋮ A high-order discontinuous Galerkin method for nonlinear sound waves ⋮ Supercloseness analysis of a stabilizer-free weak Galerkin finite element method for viscoelastic wave equations with variable coefficients ⋮ Optimal a priori error estimates for the finite element approximation of dual-phase-lag bio heat model in heterogeneous medium ⋮ Finite element method for hyperbolic heat conduction model with discontinuous coefficients in one dimension

Uses Software

• GeoPDEs

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