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Numerical Algorithms

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13-02-2023 | Original Paper

Uniform convergence of optimal order for a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation with parabolic layers

Authors: Xiaowei Liu, Jin Zhang

Published in: Numerical Algorithms | Issue 1/2023

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Abstract

This paper is to analyze a finite element method of any order on a Bakhvalov-type mesh in the case of 2D. By introducing a new interpolation according to the characteristics of layers, we show that the finite element method has uniform convergence of the optimal order with respect to the singular perturbation parameter. The result partially resolves an open problem introduced by Roos and Stynes (Comput. Methods Appl. Math. 15(4):531–550, 2015).

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Title: Uniform convergence of optimal order for a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation with parabolic layers
Authors: Xiaowei Liu
Jin Zhang
Publication date: 13-02-2023
Publisher: Springer US
Published in: Numerical Algorithms / Issue 1/2023
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-023-01508-x

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