International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 962070, 18 pages
Research Article

Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem

1Department of Mathematics, Anna University Chennai, CEG Campus, Chennai 600 025, India
2Department of Mathematics, M.N.M Jain Engineering College, Thoraipakkam, Chennai 600097, India

Received 20 July 2011; Revised 24 November 2011; Accepted 25 November 2011

Academic Editor: Attila Gilányi

Copyright © 2012 L. Jones Tarcius Doss and A. P. Nandini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.