Error analysis of an implicit-explicit time discretization scheme for semilinear wave equations with application to multiscale problems

Document detail

ID

oai:arXiv.org:2406.19889

Topic

Mathematics - Numerical Analysis 65J08, 65M60, 65M15, 65M12, 35L71

Author

Eckhardt, Daniel Hochbruck, Marlis Verfürth, Barbara

Year

2024

listing date

7/3/2024

Keywords

space

Metrics

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.

Eckhardt, Daniel,Hochbruck, Marlis,Verfürth, Barbara, 2024, Error analysis of an implicit-explicit time discretization scheme for semilinear wave equations with application to multiscale problems