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

S. Iqbal, A. Javed, A. R. Ansari, Abdul M. Siddiqui

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Article number17092672
Pages (from-to)1001-1011
Number of pages11
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Volume23
Issue number6
DOIs
StatePublished - Jul 29 2013

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Grid Refinement
Adaptive Refinement
Adaptive Grid
Obstacle Problem
Finite Element Solution
Boundary value problems
Boundary Value Problem
Error analysis
A Posteriori Error Estimation
Piecewise Linear Approximation
Galerkin Finite Element Method
Meshing
Polynomials
Finite element method
Design Methodology
Approximate Solution
Numerical Experiment
Numerical Solution
Contact
Finite Element

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

Cite this

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A spatially adaptive grid refinement scheme for the finite element solution of a second order obstacle problem. / Iqbal, S.; Javed, A.; Ansari, A. R.; Siddiqui, Abdul M.

In: International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 23, No. 6, 17092672, 29.07.2013, p. 1001-1011.

Research output: Contribution to journalArticle

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AU - Ansari, A. R.

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