An $hp$ Finite Element Method for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters
Year: 2021
Author: Irene Sykopetritou, Christos Xenophontos
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 481–499
Abstract
We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called $Spectral$ $Boundary$ $Layer$ mesh. We show that the method converges uniformly, with respect to both singular perturbation parameters, at an exponential rate when the error is measured in the energy norm. Numerical examples are also presented, which illustrate our theoretical findings as well as compare the proposed method with others found in the literature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19111
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 481–499
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Singularly perturbed problem reaction-convection-diffusion boundary layers $hp$ finite element method robust exponential convergence.