An Adaptive Finite Element Formulation for the Solution of Second Order Obstacle Problems using Quadratic Lagrange Polynomials

S. Iqbala, A. R. Ansarib1, A. Javedc and A. M. Siddiquid

aDepartment of Computer Science, COMSATS Institute of Information Technology, Sahiwal Campus, Pakistan.
bCentre for Advance Studies in Engineering (CASE), 19-Attaturk Avenue, G-5/1, Islamabad, Pakistan.
cDepartment of Mathematics & Natural Sciences, Gulf University for Science & Technology, P.O. Box 7207, Hawally 32093, Kuwait
dDepartment of Mathematics, York Campus, Pennsylvania State University, York,PA 17403, USA

Abstract: A weighted-residual based a posteriori error estimation formulation in Galerkin’s finite element fashion using quadratic Lagrange polynomials has been formulated to find numerical solutions of obstacle, unilateral and contact second-order boundary-value problems. The approach having piecewise quadratic shape functions has been utilized for checking “>the approximate solutions for spatially adaptive finite element grids. The local element balance based on the residual has been considered as an error assessment criterion. Numerical testing indicates that local errors are large at the interface regions where the gradients are large. A comparison of an adaptive refined grid with that of a uniform mesh for second order obstacle boundary value problems, confirms the superiority of the adaptive scheme without increasing the number of unknown coefficients.

Keywords: Adaptive grid re nement scheme, Quadratic Lagrange polynomials, Galerkin’s method, Finite element method, Boundary-value problems
Mathematics Subject Classi cation: 65M60

 

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