A Higher-Order Defect Correction Method Over an Adaptive Bakhvalov-Shishkin Mesh for Advection-Diffusion Equations

Aditya Kaushik; Monika Choudhary

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A Higher-Order Defect Correction Method Over an Adaptive Bakhvalov-Shishkin Mesh for Advection-Diffusion Equations

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摘要

The paper presents a defect correction method based on finite difference discretizations over a Bakhvalov-Shishkin mesh for a class of convection-diffusion equations. The technique combines a stable, low-order accurate, computationally inexpensive upwind difference scheme with a higher-order less stable modified central difference operator at several grid points. We prove that the method is second-order uniformly convergent at all mesh points. We do not use asymptotic expansions of discretization errors in our analysis. The method has no directional bias, and it can be used in an adaptive procedure to refine the mesh in the non-smooth parts. Numerical results are presented, which indicate that defect correction on layer-adapted meshes is an excellent method to achieve higher-order accuracy for singular perturbation problems.

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来源
《Iranian Journal of Science》 |2023年第4期|1221-1232|共12页
作者
Aditya Kaushik; Monika Choudhary;
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作者单位

Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India;

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原文格式 PDF
正文语种英语
中图分类自然科学理论与方法论;
关键词
Singular perturbation; Defect correction method; Finite difference; Non-uniform mesh;

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A Higher-Order Defect Correction Method Over an Adaptive Bakhvalov-Shishkin Mesh for Advection-Diffusion Equations

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