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

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ABSTRACTIn 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.