Abstract
Two dimensional elliptic reaction - diffusion problem with highly anisotropic coefficients is considered. The second order derivative with respect to one of the independent variables is multiplied by a small parameter ∈. In this work, we construct and study finite difference schemes, defined on a priori Shishkin meshes, uniformly convergent with respect to the small parameter ∈, which have order three except for a logarithmic factor. Numerical experiments confirming the theoretical results are given.
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Brayanov, I., Dimitrova, I. (2003). Uniformly Convergent High-Order Schemes for a 2D Elliptic Reaction-Diffusion Problem with Anisotropic Coefficients. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_44
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DOI: https://doi.org/10.1007/3-540-36487-0_44
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