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Indexed by:Journal Papers

Date of Publication:2021-04-26

Journal:INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Volume:98

Issue:4

Page Number:758-782

ISSN No.:0020-7160

Key Words:Nonconforming finite element; polynomial; convex quadrilateral; singular perturbation; uniform convergence

Abstract:This work proposes two nonconforming polynomial finite elements over general convex quadrilaterals. The first one is designed for fourth order elliptic singular perturbation problems, and the other works for Brinkman problems, approximating the velocity with piecewise constant pressure. We show the robustness of these methods, namely, the discrete solution converges uniformly in the given parameters of the corresponding model problem. Numerical examples are also provided.