A Quadrature Finite Element Galerkin Scheme for a Biharmonic Problem on a Rectangular Polygon
نویسنده
چکیده
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 00: 000–000, 2007
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