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

Iranian Journal of Numerical Analysis and Optimization

مقاله 9، دوره 14، Issue 1 - شماره پیاپی 28، خرداد 2024، صفحه 219-264   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.84272.1311

نویسندگان

K. K. Sah^* ؛ S. Gowrisankar

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

چکیده

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.

کلیدواژه‌ها

Singularly perturbed parabolic problem؛ Regular boundary layer؛ Upwind scheme؛ Richardson extrapolation؛ Modified graded mesh؛ Uniform convergence

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