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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

verfasst von: Xiaowei Liu, Jin Zhang

Erschienen in: Numerical Algorithms | Ausgabe 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).

Vorheriger Artikel Second-order partitioned method and adaptive time step algorithms for the nonstationary Stokes-Darcy equations

Nächster Artikel Inexact asymmetric forward-backward-adjoint splitting algorithms for saddle point problems

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Titel: 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
verfasst von: Xiaowei Liu
Jin Zhang
Publikationsdatum: 13.02.2023
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 1/2023
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-023-01508-x

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