2021
DOI: 10.48550/arxiv.2109.09429
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Convergence analysis of an operator-compressed multiscale finite element method for Schrödinger equations with multiscale potentials

Zhizhang Wu,
Zhiwen Zhang

Abstract: In this paper, we analyze the convergence of the operator-compressed multiscale finite element method (OC MsFEM) for Schrödinger equations with general multiscale potentials in the semiclassical regime. In the OC MsFEM the multiscale basis functions are constructed by solving a constrained energy minimization. Under a mild assumption on the mesh size H, we prove the exponential decay of the multiscale basis functions so that localized multiscale basis functions can be constructed, which achieve the same accura… Show more

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