Abstract
In this work we solve efficiently 2D time dependent singularly perturbed problems. The fully discrete numerical scheme is constructed by using a two step discretization process, firstly in space, by using the classical upwind finite difference scheme on a special mesh of Shishkin type, and later on in time by using the fractional implicit Euler method. The method is uniformly convergent with respect to the diffusion parameter having first order in time and almost first order in space. We focus our interest on the analysis of the influence of general Dirichlet boundary conditions in the convergence of the algorithm. We propose a simple modification of the natural evaluations, which avoid the order reduction associated to those natural evaluations. Some numerical tests are shown in order to exhibit, from a practical of point of view, the robustness of the numerical method as well as the influence of the improved boundary conditions.
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References
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Acknowledgements
This research was partially supported by the project MTM2014-52859 and the Diputación General de Aragón.
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Clavero, C., Jorge, J.C. (2017). Order Reduction and Uniform Convergence of an Alternating Direction Method for Solving 2D Time Dependent Convection-Diffusion Problems. In: Huang, Z., Stynes, M., Zhang, Z. (eds) Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. Lecture Notes in Computational Science and Engineering, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-319-67202-1_4
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DOI: https://doi.org/10.1007/978-3-319-67202-1_4
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