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Analysis of a DG method for singularly perturbed convection-diffusion problems
Runchang Lin,Xiu Ye,Shangyou Zhang,Peng Zhu
Keywords:Discontinuous Galerkin, finite element method, convection-diffusion-reaction problem, singular perturbation, polyhedral mesh
Abstract:
      In this article, we studied a discontinuous Galerkin finite element method for convection-diffusion-reaction problems with singular perturbation. Our approach is highly flexible by allowing the use of discontinuous approximating function on polytopal mesh without imposing extra conditions on the convection coefficient. {\em A priori} error estimate is devised in a suitable energy norm on general polytopal mesh. Numerical examples are provided.