A generalized finite element method for the strongly damped wave equation with rapidly varying data
Artikel i vetenskaplig tidskrift, 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

Författare

Per Ljung

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Axel Målqvist

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Anna Persson

Kungliga Tekniska Högskolan (KTH)

Mathematical Modelling and Numerical Analysis

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

Vol. 55 4 1375-1403

Ämneskategorier

Teknisk mekanik

Beräkningsmatematik

Matematisk analys

DOI

10.1051/m2an/2021023

Mer information

Senast uppdaterat

2021-07-28