 A computational method for a two-parameter singularly perturbed elliptic problem with boundary and interior layersRam Shiromani, Vembu Shanthi and Higinio Ramos Mathematics and Computers in Simulation (MATCOM), 2023, vol. 206, issue C, 40-64 Abstract: In this article, we investigate a two-dimensional (2-D) singularly perturbed convection–reaction–diffusion elliptic type problem where two parameters ϵ and μ multiply the diffusion and convection terms, respectively. Furthermore, we assume that jump discontinuities exist in the source term along the x- and y-axis. Due to the presence of perturbation parameters, the solutions to such problems show boundary and corner layers. Moreover, the discontinuity in the source term adds the interior layers to the solution whose suitable numerical approach is the important goal of this article. A numerical approach is carried out using an upwind finite-difference technique that includes an appropriate layer-adapted piecewise uniform Shishkin mesh. Some examples are presented which show the good performance of the proposed method and the agreement with the theoretical analysis. Keywords: Discontinuous source term; Finite-difference method; Shishkin mesh; Elliptic equation; Two singular perturbation parameters; Two dimensional space (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:206:y:2023:i:c:p:40-64 DOI: 10.1016/j.matcom.2022.11.003 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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