Adaptive refinement for convection-diffusion problems based on a defect-correction technique and finite difference method |
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Authors: | O Axelsson M Nikolova |
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Affiliation: | 1. Faculty of Mathematics and Informatics, University of Nijmegen, NL-6525, ED Nijmegen, The Netherlands
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Abstract: | A difference method is presented for singularly perturbed convection-diffusion problems with discretization error estimates of high order (orderp), which hold uniformly in the singular perturbation parameterε. The method is based on the use of a defect-correction technique and special adaptively graded and patched meshes, with meshsizes varying betweenh andε 3/2 h whenp=2, whereh is the meshsize, used in the part of the domain where the solution is smooth, andε 3/2 h is the final meshsize in the boundary layer. Similar constructions hold for interior layers. The correction operator is a monotone operator, enabling the estimate of the error of optimal order in maximum norm. The total number of meshpoints used in ad-dimensional problem isO(ε ?s)h ?d+O(h ?d), wheres is 1/p or 1/2p, respectively in the case of boundary or interior layer. |
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