Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

Lijian Jiang, Yalchin R. Efendiev, Victor Ginting

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Original languageEnglish (US)
Pages (from-to)862-876
Number of pages15
JournalApplied Numerical Mathematics
Volume60
Issue number8
DOIs
StatePublished - Aug 2010
Externally publishedYes

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