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- W2483283551 abstract "In this work we deal with a different technique from the considered one in Clavero et al. (IMA J Numer Anal 26:155–172, 2006; Appl Numer Math 27:211–231, 1998), to analyze the uniform convergence of some numerical methods which have been used to solve successfully two dimensional parabolic singularly perturbed problems of convection-diffusion type. For getting this, we split the discretization methods in a two stage procedure where, firstly, we semidiscretize in space, using the classical upwind scheme on a piecewise uniform Shishkin mesh, and, secondly, we integrate in time the Initial Value Problems derived from the first stage, by using the implicit Euler method. The analysis combines a suitable maximum semidiscrete principle joint to some well known techniques used in the proof of the uniform convergence of numerical schemes for elliptic singularly perturbed problems. We prove that the stiff initial value problems resulting of the spatial semidiscretization processes, have a unique solution which converges uniformly with respect to the singular perturbation parameter. Using this technique, some restrictions among the discretization parameters, which appeared in the uniform convergence analysis in Clavero et al. (Appl Numer Math 27:211–231, 1998), can be removed. Some numerical results corroborate in practice the robustness of the numerical method, according to the theoretical results." @default.
- W2483283551 created "2016-08-23" @default.
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- W2483283551 date "2015-01-01" @default.
- W2483283551 modified "2023-10-02" @default.
- W2483283551 title "Spatial Semidiscretizations and Time Integration of 2D Parabolic Singularly Perturbed Problems" @default.
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- W2483283551 doi "https://doi.org/10.1007/978-3-319-25727-3_6" @default.
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