Optimal Error Estimates for a Singularly Perturbed Parabolic Interface Problem with a Weak Galerkin Method in Space and Forward Euler Scheme in Time

In this article, we are concerned with designing a numerical approximation for solving a singularly perturbed parabolic interface problem via the weak Galerkin finite element technique in space and an explicit method in time. Firstly, the spatial discretization is made using the local \((P_k(N),P_k(e),[Pₖ₋₁(N)]^2)\) weak Galerkin element and then forward Euler method is utilized for temporal discretization. The optimal order of convergence is obtained theoretically in the energy and L² norms for both the semi-discrete and fully-discrete problems. Some numerical experiments are presented to validate the theoretical error estimates.