A domain decomposition Taylor Galerkin finite element approximation of a parabolic singularly perturbed differential equation

In this paper, we deal with a discrete Monotone Iterative Domain Decomposition (MIDD) method based on Schwarz alternating algorithm for solving parabolic singularly perturbed partial differential equations. A discrete iterative algorithm is proposed which combines the monotone approach and the iterative non-overlapping Domain Decomposition Method (DDM) based on the Schwarz alternating procedure using three-step Taylor Galerkin Finite Element (3TGFE) approximation for solving parabolic singularly perturbed partial differential equations. The subdomain boundary conditions are updated through well defined interface problems. The convergence of the MIDD method has been established. Further, the proposed 3TGFE based MIDD method has been successfully implemented on three test problems.