Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 13...
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| Autores principales: | , , |
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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v32_n2_p511_Duran http://hdl.handle.net/20.500.12110/paper_02724979_v32_n2_p511_Duran |
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| Sumario: | In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution. © The author 2011. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. |
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