Supercloseness Result of Higher Order FEM/LDG Coupled Method for Solving Singularly Perturbed Problem on S-Type Mesh

Abstract

we present a first supercloseness analysis for higher order FEM/LDG coupled method for solving singularly perturbed convection-diffusion problem. Based on piecewise polynomial approximations of degree $k$ $(k\ge 1)$, a supercloseness property of $k+1/2$ in DG norm is established on S-type mesh. Numerical experiments complement the theoretical results.