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A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon
Author(s) -
Aitbayev Rakhim
Publication year - 2008
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.20278
Subject(s) - mathematics , biharmonic equation , quadrature (astronomy) , galerkin method , gaussian quadrature , mathematical analysis , rate of convergence , finite element method , boundary value problem , nyström method , channel (broadcasting) , physics , electrical engineering , engineering , thermodynamics
Abstract A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008