Convergence analysis of a fully-discrete FEM for singularly perturbed two-parameter parabolic PDE

被引：4

作者：

Avijit, D. ^{[1
]}

Natesan, S. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Gauhati 781039, India

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2022年 / 197卷

关键词：

Singularly perturbed 1D two-parameter parabolic PDEs; Streamline-diffusion finite element method; Bakhvalov-type mesh; Shishkin; mesh; Exponentially graded mesh; Stability; Error analysis; BOUNDARY-VALUE-PROBLEMS; ERROR ANALYSIS; 2; PARAMETERS; DIFFUSION; SCHEME; MESH; SDFEM;

D O I：

10.1016/j.matcom.2022.02.005

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This article deals with the numerical solution of a singularly perturbed initial-boundary value problem (IBVP) with two parameters on a rectangular space-time domain. A fully-discrete numerical method by combining the Crank-Nicolson scheme for temporal derivative and the streamline-diffusion finite element method (SDFEM) for spatial derivatives has been established in a new theoretical framework. A suitable stabilization parameter has been explored on some conditions related to error analysis. The robust error estimates and the stability results are obtained by using P1-finite element in the discrete L2(0, T; SD)-norm. Theoretical results are verified by some numerical experiments. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：185 / 206

页数：22

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