A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon | Zendy

Aitbayev Rakhim | Zendy

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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

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

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