Applications of Gauss-Radau and Gauss-Lobatto Numerical Integrations Over a Four Node Quadrilateral Finite Element

Abstract

In this paper Gauss-Radau and Gauss-Lobatto quadrature rules are presented to evaluate the rational integrals of the element matrix for a general quadrilateral. These integrals arise in finite element formulation for second order Partial Differential Equation via Galerkin weighted residual method in closed form. Convergence to the analytical solutions and efficiency are depicted by numerical example. Key words: Gauss-Radau, Gauss-Lobatto, Rational Integrals, Quadrilateral Finite Element.  DOI = 10.3329/bjsir.v43i3.1153 Bangladesh J. Sci. Ind. Res. 43(3), 377-386, 2008