Integration pointwise pollution error estimates in the finite element method in one dimension

Authors:
G. Tsamasphyros;S. Markolefas
Affiliations:
Department of Applied Mechanics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, 9 Iroon Polytechniou, Zografou 157 73, Athens, Greece;Department of Applied Mechanics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, 9 Iroon Polytechniou, Zografou 157 73, Athens, Greece
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

An a priori estimate for the pointwise pollution effect caused by the approximate integration is given. Furthermore, a bound for the integration perturbation error in the H1 norm is derived, for general problems satisfying the inf-sup stability condition and quasi-uniform h-extension meshes. In the numerical studies a problem with singular exact solution is discussed. The example aims at exploring how the pollution (from the numerical integration of the singular force vector), influences the accuracy and the rates of convergence (of both h- and p-versions) of the finite element method. Finally, for the purpose of verification of the pointwise pollution error estimate, numerical results from two additional problems with smooth exact solutions are presented.