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

Document Type : Research Article

Authors

• K. K. Sah
• S. Gowrisankar

Department of Mathematics, National Institute of Technology Patna, Patna - 800005, India.

10.22067/ijnao.2023.84272.1311

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

Main Subjects

• Computational Mathematics

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