Volume 55, Number 4, July-August 2021
|Page(s)||1375 - 1404|
|Published online||07 July 2021|
A generalized finite element method for the strongly damped wave equation with rapidly varying data
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden
2 Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
* Corresponding author: firstname.lastname@example.org
Accepted: 17 May 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 Målqvist 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.
Mathematics Subject Classification: 35K10 / 65M60
Key words: Strongly damped wave equation / multiscale / localized orthogonal decomposition / finite element method / reduced basis method
© The authors. Published by EDP Sciences, SMAI 2021
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