Abstract
In this paper, we investigate the convergence of discontinuous Galerkin finite element method (DGFEM) for singularly perturbed convection-diffusion problem with discontinuous convection coefficient. Due to the discontinuity in the convection coefficient, the problem typically shows a weak interior layer. We develop a kind of DGFEM, the non-symmetric discontinuous Galerkin finite element method with interior penalties (NIPG) to handle the layer setbacks. With the use of a typical Shishkin mesh, the domain is discretized and uniform error estimate is obtained and theoretically we have obtained the convergence of order \(\mathcal {O}(N^{-1} \ln N)\). The numerical outcome backs up our theoretical conclusions.
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Ranjan, K.R., Gowrisankar, S. (2023). NIPG Method on Shishkin Mesh for Singularly Perturbed Convection-Diffusion Problem with Discontinuous Convection Coefficient. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2022. Lecture Notes in Networks and Systems, vol 666. Springer, Cham. https://doi.org/10.1007/978-3-031-29959-9_12
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