Publication

MATHICSE Technical Report : A priori error analysis of the finite element heterogenenous multiscale method for the wave equation in heterogenenous media over long time

2015
Working Papers

Abstract

A fully discrete a priori analysis of the finite element heterogenenous multiscale method (FE-HMM) introduced in [A. Abdulle, M. Grote, C. Stohrer, MultiscaleModel. Simul. 2014] for the wave equation with highly oscillatory coefficients over long time is presented. A sharpa priori convergence rate for the numerical method is derived for long time intervals. The effective model over long time is a Boussinesq-type equation that has been shown to approximate the one-dimensional multiscale wave equation with ε-periodic coefficients up to timeO(ε−2) in [Lamacz, Math. Models Methods Appl. Sci., 2011]. In this paper we also revisit this result by deriving and analysing a family of effective Boussinesq-type equations for the approximation of the multiscale wave equation that depends on the normalization chosen for certain micro functions used to define the macroscopic models.

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https://infoscience.epfl.ch/entities/publication/6d7e10d6-0784-4c6a-b9c0-0234320f8c5c

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2015
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6d7e10d6-0784-4c6a-b9c0-0234320f8c5c

About this result

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Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

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Related publications (32)

MATHICSE Technical Report : A priori error analysis of the finite element heterogenenous multiscale method for the wave equation in heterogenenous media over long time

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