Numerical solution of a mixed singularly perturbed parabolic-elliptic problem |
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Authors: | Iliya A Brayanov |
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Institution: | Department of Applied Mathematics and Informatics, University of Rousse, Studentska str. 8, 7017 Rousse, Bulgaria |
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Abstract: | A one-dimensional singularly perturbed problem of mixed type is considered. The domain under consideration is partitioned into two subdomains. In the first subdomain a parabolic reaction-diffusion problem is given and in the second one an elliptic convection-diffusion-reaction problem. The solution is decomposed into regular and singular components. The problem is discretized using an inverse-monotone finite volume method on condensed Shishkin meshes. We establish an almost second-order global pointwise convergence in the space variable, that is uniform with respect to the perturbation parameter. |
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Keywords: | Parabolic-elliptic problems Convection-diffusion problems Singular perturbation Asymptotic analysis Finite volume methods Modified upwind approximations Uniform convergence Shishkin mesh |
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