A SDFEM for system of two singularly perturbed problems of convection-diffusion type with discontinuous source term

2021/04/08 by Babu, A. Ramesh
#34M60 #FOS: Mathematics #G.1.7 #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2104.03578

Abstract

We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit boundary layers as well as weak interior layers. A numerical method based on finite element method (Shishkin and Bakhvalov-Shishkin meshes) is presented. We derive an error estimate of order O(N^-1ln^3/2N) in the energy norm with respect to the perturbation parameter. Numerical experiments are also presented to support our theoretical results.

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