A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction-diffusion problems with arbitrary small diffusion terms

Shakti, Deepti ¹Mohapatra, Jugal ²Das, Pratibhamoy ³Vigo-Aguiar, Jesus⁴

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作者信息

1. Vellore Inst Technol
2. Natl Inst Technol Rourkela
3. Indian Inst Technol
4. Univ Salamanca
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Abstract

In this paper, a system of time dependent boundary layer originated reaction dominated problems with diffusion parameters of different magnitudes, is considered for numerical analysis. The presence of these parameters lead to the boundary layer phenomena. Here, an optimal order uniformly accurate boundary layer adaptive method moving mesh method is proposed. This method is able to capture the layer phenomena without using a priori information of the solution. The problem is discretized by a modified implicit-Euler scheme in time direction. For the present system, adaptive mesh generation is required in space due to the singularly perturbed nature of the problem. For this purpose, a positive error monitor function is used whose equidistribution will move the mesh points towards the boundary layers. Parameter uniform error estimates are derived to show that the convergence rate is optimal with respect to the problem discretization. Numerical experiments strongly verify the theoretical findings and confirm the efficiency and accuracy of the proposed method. (C)& nbsp;2020 Elsevier B.V. All rights reserved.

Key words

Adaptive moving mesh/r-refinement method/Boundary layer/Coupled system of PDEs/Singularly perturbed problem/Modified implicit Euler scheme/Parabolic system of reaction-diffusion problems/B-SPLINE COLLOCATION/DIFFERENTIAL-EQUATIONS/NUMERICAL-METHOD/COUPLED SYSTEM/APPROXIMATIONS/GENERATION/ALGORITHM/SCHEME

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出版年

2022

Journal of Computational and Applied Mathematics

EISCI

ISSN：0377-0427

被引量36

参考文献量46

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