A generalized finite element method for the strongly damped wave\n equation with rapidly varying data

2020/11/06 by Per Ljung, Ljung, Per, Axel Målqvist +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2011.03311

Abstract

We propose a generalized finite element method for the strongly damped wave\nequation with highly varying coefficients. The proposed method is based on the\nlocalized orthogonal decomposition introduced and is designed to handle\nindependent variations in both the damping and the wave propagation speed\nrespectively. The method does so by automatically correcting for the damping in\nthe transient phase and for the propagation speed in the steady state phase.\nConvergence of optimal order is proven in L₂(H¹)-norm, independent of the\nderivatives of the coefficients. We present numerical examples that confirm the\ntheoretical findings.\n

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