Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

DOI10.1007/s11425-020-1857-5zbMath1493.65147arXiv2103.04700OpenAlexW3200434296MaRDI QIDQ2158851

Waixiang Cao, Dongfang Li, Zhimin Zhang

Publication date: 26 July 2022

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.04700

zbMATH Keywords

stabilitysuperconvergenceerror estimatewave equationsscalar auxiliary variable

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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)

Related Items (7)

A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation ⋮ Relaxation Exponential Rosenbrock-Type Methods for Oscillatory Hamiltonian Systems ⋮ Crank-Nicolson compact difference schemes and their efficient implementations for a class of nonlocal nonlinear parabolic problems ⋮ Linearly implicit and high-order energy-preserving relaxation schemes for highly oscillatory Hamiltonian systems ⋮ One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations ⋮ Global quantitative stability of wave equations with strong and weak dampings ⋮ Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations

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