Year: 2026
Type: article
Abstract: . In this paper, we investigate the approximation properties of two types of multiscale finite element methods with oversampling as proposed in [Hou and Wu, J. Comput. Phys., 134 (1997), pp. 169–189] and [Efendiev, Hou, and Wu, SIAM J. Numer. Anal., 37 (2000), pp. 888–910] without scale separation. We develop a general interpolation error analysis for elliptic problems with highly oscillatory rough coefficients, under the assumption of the existence of a macroscopic problem with suitable [Formula: see text]-accuracy. The distinct features of the analysis, in the setting of highly oscillatory periodic coefficients, include the following: (i) the analysis is independent of the first-order corrector or the solutions to the cell problems, and thus independent of their regularity properties; and (ii) the analysis only involves the homogenized solution and its minimal regularity. We derive an interpolation error [Formula: see text] with [Formula: see text] and [Formula: see text] being the period size and the coarse mesh size, respectively, when the oversampling domain includes one layer of elements from the target coarse element.
DOI: 10.1137/25m1779954
Author: Guanglian Li
Institution: University of Hong Kong
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417429873
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