No abstract

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, 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, independent of the derivatives of the coefficients. We present numerical examples that confirm the theoretical findings.

In this presentation we study numerical solutions to a parabolic equation where the diffusion varies rapidly in both space and time. This type of equation, i.e. where the coefficient is highly varying, is commonly referred to as a multiscale equation, and it generally appears in the modelling of, for example, porous medium or composite materials. The parabolic equation arises in several real life applications, such as heat transfer and modelling of pressure in compressible flow. In particular, the time-dependency in the diffusion becomes of significance when considering a head conductor undertaking radioactive decay [3].