Numerical Homogenization of Elliptic PDEs with Similar Coefficients
Artikel i vetenskaplig tidskrift, 2019

We consider a sequence of elliptic partial differential equations (PDEs) with different but similar rapidly varying coefficients. Such sequences appear, for example, in splitting schemes for time-dependent problems (with one coefficient per time step) and in sample based stochastic integration of outputs from an elliptic PDE (with one coefficient per sample member). We propose a parallelizable algorithm based on Petrov-Galerkin localized orthogonal decomposition that adaptively (using computable and theoretically derived error indicators) recomputes the local corrector problems only where it improves accuracy. The method is illustrated in detail by an example of a time-dependent two-pase Darcy flow problem in three dimensions.

elliptic PDEs

time-dependent PDEs

finite element method

numerical homogenization

Författare

Fredrik Hellman

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Uppsala universitet

Axel Målqvist

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Multiscale Modeling and Simulation

1540-3459 (ISSN)

Vol. 17 2 650-674

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

10.1137/18M1189701

Mer information

Senast uppdaterat

2019-11-11