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Indexed by:期刊论文

Date of Publication:2018-12-11

Journal:ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Included Journals:SCIE

Volume:52

Issue:5

Page Number:1981-2001

ISSN No.:0764-583X

Key Words:Singular perturbation problem; quadrilateral element; uniformly convergent

Abstract:In this paper, a C-0 nonconforming quadrilateral element is proposed to solve the fourthorder elliptic singular perturbation problem. For each convex quadrilateral Q, the shape function space is the union of S-2(1) (Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.