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Indexed by:期刊论文
Date of Publication:2018-01-01
Journal:JOURNAL OF SCIENTIFIC COMPUTING
Included Journals:SCIE、EI、Scopus
Volume:74
Issue:1
Page Number:324-335
ISSN No.:0885-7474
Key Words:Nonconforming element; Nonparametric; Finite element; Quadrilateral mesh
Abstract:In this paper, a new nonparametric nonconforming quadrilateral finite element is introduced. This element takes the four edge mean values as the degrees of the freedom and the finite element space is a subspace of . Different from the other nonparametric elements, the basis functions of this new element can be expressed explicitly without solving linear systems locally, which can be achieved by introducing a new reference quadrilateral. To evaluate the integration, a class of new quadrature formulae with only three equally weighted points on quadrilateral are constructed. Hence the stiffness matrix can be calculated by the same way with the parametric elements. Numerical results are shown to confirm the optimality of the convergence order for the second order elliptic problems and the Stokes problem.