Discontinuous Galerkin approach for two parametric convection-diffusion equation with discontinuous source term

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 11 دی 1402   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.84456.1316

نویسندگان

Kumar Rajeev Ranjan^* ؛ Dr. Gowrisankar S

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

چکیده

In this article, we explore the discontinuous Galerkin finite element method (DGFEM) for two-parametric singularly perturbed convection-diffusion problems with a discontinuous source term. Due to the discontinuity in the source term, the problem typically shows a weak interior layer. Also, the presence of the multiple perturbation parameters in the problem cause boundary layers on both the sides of the boundary. In this work we develop the non-symmetric discontinuous Galerkin finite element method with interior penalties (NIPG) to handle the layer phenomenon. With the use of a typical Shishkin mesh, the domain is discretized and uniform error estimate is obtained. The numerical experiments are conducted to validate the theoretical conclusions.

کلیدواژه‌ها

Convection-diffusion problem؛ The NIPG methods؛ Shishkin mesh؛ Interior layers؛ Uniform convergence