Parameter-uniform numerical method for a two-dimensional singularly perturbed convection–reaction–diffusion problem with interior and boundary layers

S. Chandra Sekhara Rao and Abhay Kumar Chaturvedi

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 187, issue C, 656-686

Abstract: We consider a two-dimensional singularly perturbed convection–reaction–diffusion problem that has discontinuities, along lines parallel to x- and y-axes, in the source term, as well as in the convection and reaction coefficients. The coefficient of the highest-order term is a small positive parameter denoted by ε. Due to the discontinuities, the solution exhibits layers in the interior of the domain, in addition to boundary layers. We propose a decomposition of the solution that yields sharp bounds on its derivatives. A finite difference scheme is constructed on an appropriate Shishkin mesh, and it is established that the computed solution is almost first-order, parameter-uniformly convergent. Numerical results are given to support the theoretical results.

Keywords: Singular perturbation; Convection–reaction–diffusion; Interior layers; Corner layers; Boundary layers; Shishkin mesh; Finite difference method; Parameter-uniform convergence (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:187:y:2021:i:c:p:656-686

DOI: 10.1016/j.matcom.2021.03.016

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