A spatially adaptive grid refinement scheme for the finite element solution of a second order obstacle problem

Abstract

Purpose

The authors' objective in this paper is to find the numerical solutions of obstacle, unilateral and contact second‐order boundary‐value problems.

Design/methodology/approach

To achieve this, the authors formulate a spatially adaptive grid refinement scheme following Galerkin's finite element method based on a weighted‐residual. A residual based a‐posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local element balance has been considered as an error assessment criterion. The approach utilizes piece‐wise linear approximations utilizing linear Langrange polynomials. Numerical experiments indicate that local errors are large in regions where the gradients are large.

Findings

A comparison of the spatially adaptive grid refinement with that of uniform meshing for second order obstacle boundary value problems confirms the superiority of the scheme without increasing the number of unknown coefficients.

Originality/value

The authors believe the work has merit not only in terms of the approach but also of the problem solved in the paper.

Citation

Iqbal, S., Javed, A., Ansari, A.R. and Siddiqui, A.M. (2013), "A spatially adaptive grid refinement scheme for the finite element solution of a second order obstacle problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 6, pp. 1001-1011. https://doi.org/10.1108/HFF-10-2011-0212