Year: 2017
Type: preprint
Abstract: We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of the media is constructed by solving finite-dimensional localized problems. The method requires $O(log(1/H)^{d+1})$ basis functions per mesh point. We prove that the optimal finite element convergence rates are preserved.
Source: arXiv (Cornell University)
Author: Weymuth, Monika
Institution: University of Zurich
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2956858360