Richardson extrapolation technique on a modified graded mesh for singularly perturbed parabolic convection-diffusion problems

Abstract

In this paper, we focus on investigating a post-processing technique de-signed for one-dimensional singularly perturbed parabolic convection-diffusion problems that demonstrate a regular boundary layer. We use a back-ward Euler numerical approach for time derivatives with uniform mesh in the temporal direction, and a simple upwind scheme is used for spa-tial derivatives with modified graded mesh in the spatial direction. In this study, we demonstrate the effectiveness of the Richardson extrapola-tion technique in enhancing the ε-uniform accuracy of simple upwinding within the discrete supremum norm, as evidenced by an improvement from O(N −1 ln(1/ε) + △θ) to O(N −2 ln2(1/ε) + △θ2). Furthermore, to validate the theoretical findings, computational experiments are conducted for two test examples by applying the proposed technique.

Keywords

• singularly perturbed parabolic problem
• regular boundary layer
• upwind scheme
• richardson extrapolation
• modified graded mesh
• uniform convergence