A generalized finite element method for the strongly damped wave equation with rapidly varying data
Journal article, 2021

We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced in Malqvist and Peterseim [Math. Comp. 83 (2014) 2583-2603], and is designed to handle independent variations in both the damping and the wave propagation speed respectively. The method does so by automatically correcting for the damping in the transient phase and for the propagation speed in the steady state phase. Convergence of optimal order is proven in L2(H1)-norm, independent of the derivatives of the coefficients. We present numerical examples that confirm the theoretical findings.

Strongly damped wave equation

Reduced basis method

Localized orthogonal decomposition

Finite element method

Multiscale

Author

Per Ljung

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Axel Målqvist

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Anna Persson

Royal Institute of Technology (KTH)

Mathematical Modelling and Numerical Analysis

0764-583X (ISSN) 1290-3841 (eISSN)

Vol. 55 4 1375-1403

Subject Categories

Applied Mechanics

Computational Mathematics

Mathematical Analysis

DOI

10.1051/m2an/2021023

More information

Latest update

7/28/2021