Galerkin's finite element formulation of the second-order boundary-value problems

Abstract

A Galerkin's finite element approach based on weighted-residual formulation is presented to find approximate solutions to obstacle, unilateral and contact second-order boundary-value problems. The approach utilizes a piece-wise linear approximations utilizing linear Langrange polynomials. Numerical studies have shown the superior accuracy and lesser computational cost of this scheme in comparison to collocation, finite-difference and spline methods.

Keywords:

• Galerkin method
• finite element method
• boundary-value problems

2000 AMS Subject Classifications :

• 65M60
• 80M10
• 65L10

Acknowledgements

The authors wish to thank Prof. Dr Muhammad Aslam Noor, Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan, for his valuable suggestions in the preparation of this manuscript.