Error analysis of an implicit-explicit time discretization scheme for semilinear wave equations with application to multiscale problems
Numerical Analysis
2024-07-01 v1 Numerical Analysis
Abstract
We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally stable but also highly efficient. Our main results are error bounds of the full discretization in space and time for the IMEX scheme combined with a general abstract space discretization. As an application, we consider the heterogeneous multiscale method for wave equations with highly oscillating coefficients in space for which we show spatial and temporal convergence rates by using the abstract result.
Keywords
Cite
@article{arxiv.2406.19889,
title = {Error analysis of an implicit-explicit time discretization scheme for semilinear wave equations with application to multiscale problems},
author = {Daniel Eckhardt and Marlis Hochbruck and Barbara Verfürth},
journal= {arXiv preprint arXiv:2406.19889},
year = {2024}
}