# KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

## Assyr Abdulle, Swiss Federal Institute of Technology in Lausanne (Switzerland) Finite Element Heterogeneous Multiscale Method for the Wave Equation

• A. Abdulle
• M. Grote
• C. Stohrer

### Abstract

Following the framework of the heterogeneous multiscale method, we present a finite element method for wave propagation in heterogeneous media (modeled by the wave equation with highly oscillatory coefficients). The numerical method is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coefficients are computed on sampling domains at the micro scale within each macro finite element. Optimal fully discrete error estimates in the energy norm and the $$L^{2}$$ norm and convergence to the homogenized problem are given.

Numerical examples confirm the theoretical convergence rates and illustrate the performance and versatility of our approach.