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Journal Articles Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Year : 2022

An MsFEM approach enriched using Legendre polynomials

Abstract

We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A convergence analysis of the approach is presented. Residue-type a posteriori error estimates are also established. Numerical experiments show a significant reduction in the error at a limited additional off-line cost. In particular, the approach developed here is less prone to resonance errors in the regime where the coarse mesh size $H$ is of the order of the small scale $\varepsilon$ of the oscillations.

Dates and versions

hal-03333670 , version 1 (03-09-2021)

Identifiers

Cite

Frederic Legoll, Pierre-Loik Rothé, Claude Le Bris, Ulrich Hetmaniuk. An MsFEM approach enriched using Legendre polynomials. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2022, 20 (2), pp.798-834. ⟨10.1137/21M1444151⟩. ⟨hal-03333670⟩
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