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A new quadratic nonconforming finite element on rectangles
Author(s) -
Lee Heejeong,
Sheen Dongwoo
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20131
Subject(s) - mathematics , rectangle , finite element method , degrees of freedom (physics and chemistry) , quadratic equation , mathematical analysis , interpolation (computer graphics) , function (biology) , geometry , image (mathematics) , physics , quantum mechanics , evolutionary biology , biology , computer science , thermodynamics , artificial intelligence
A new quadratic nonconforming finite element on rectangles (or parallelograms) is introduced. The nonconforming element consists of P 2 ⊕ Span{ x 2 y , x y 2 } on a rectangle and eight degrees of freedom. Our element is essentially of seven degrees of freedom since the degree of freedom associated with the integration on rectangle is essentially of bubble‐function nature. Global basis functions are constructed for both Dirichlet and Neumann type of problems; accordingly the corresponding dimensions are counted. The local and global interpolation operators are defined. Error estimates of optimal order are derived in both broken energy and L 2 (Ω) norms for second‐order of elliptic problems. Brief numerical results are also shown to confirm the optimality of the presented quadratic nonconforming element. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006