Shishkin-type mesh plays an important role in uniform convergent numerical method for singularly perturbed problem. But usually it is hard to prove the uniform convergence of high order finite element method on Shishkin-type mesh. In this talk, we will introduce two approaches to analysis uniform convergence of high order IPDG method for singularly perturbed problem of convection diffusion type. The first approach is "a special interpolation plus Shishkin-type mesh" and the second approach is "a standard Lagrange interpolation plus Graded mesh".

Dr. Peng Zhu obtained his PhD in Computational Mathematics at the Hunan University, China, in 2010. Currently he is working as associate professor at Jiaxing University. His research interests are stabilized finite element methods (such as discontinuous Galerkin method, weak Galerkin method) for convection-dominated problems.