A Novel ADI-Weak Galerkin Method for Singularly Perturbed Two-Parameter 2D Parabolic Pdes

被引:0
|
作者
Raina, Aayushman [1 ]
Natesan, Srinivasan [1 ]
Toprakseven, Suayip [2 ]
机构
[1] Indian Inst Technol Guwahati, Dept Math, Gauhati, India
[2] Yozgat Bozok Univ, Fac Art & Sci, Dept Math, Yozgat, Turkiye
关键词
ADI-type method; convergence analysis; operator-splitting method; piecewise-uniform shishkin mesh; singularly perturbed 2D parabolic convection-reaction-diffusion problem; stability; WG-FEM; CONVECTION-DIFFUSION PROBLEMS; FRACTIONAL-STEP METHOD; FINITE-ELEMENT-METHOD; NUMERICAL-METHODS; CONVERGENCE; STABILITY; BOUNDARY; MESH;
D O I
10.1002/num.23169
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we propose an Alternating Direction Implicit (ADI) type operator splitting weak Galerkin finite element method (WG-FEM) for solving a parabolic singularly perturbed problem with two-parameters in 2D over a layer-adapted mesh. The suggested operator splitting approach divides the original model problem into two subproblems each in 1D, then solving each subproblem using WG-FEM in spatial direction eventually reduces the computational difficulty and high storage requirements. Backward-Euler time discretization has been taken over a uniform mesh. Stability and convergence results have been proved for the fully-discrete scheme. Numerical examples are presented corroborating in practice our theoretical findings.
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页数:22
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