Numerical Homogenization of Elliptic PDEs with Similar Coefficients
Journal article, 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

Author

Fredrik Hellman

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Uppsala University

Axel Målqvist

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Multiscale Modeling and Simulation

1540-3459 (ISSN) 15403467 (eISSN)

Vol. 17 2 650-674

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.1137/18M1189701

More information

Latest update

11/11/2019