An MsFEM Approach Enriched Using Legendre Polynomials
Frédéric Legoll, Pierre-Loïk Rothé, Claude Le Bris, Ulrich L. Hetmaniuk · Multiscale Modeling and Simulation · 2022
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 [Formula: see text] is of the order of the small scale [Formula: see text] of the oscillations.