报告题目：High order symmetric direct discontinuous Galerkin method for elliptic interface problems with fitted mesh
报告人：Jue YAN 副教授，Iowa State University
In this talk I will discuss the newly developed symmetric direct discontinuous Galerkin (DDG) method for the elliptic interface problems associated with solution jump and flux jump interface conditions. We focus on the case with mesh partition aligning with the curved interface. Numerical fluxes on the edges of curved triangular elements that overlap with the interface are carefully designed. Both the solution jump and flux jump conditions are incorporated into numerical flux definitions and enforced in the weak sense and a stable and high order method is obtained. Optimal $(k+1)th$ order $L^2$ norm error estimate is proved for polygonal interface. A sequence of numerical examples are carried out to verify the optimal convergence of the symmetric DDG method with high order $P_2$, $P_3$ and $P_4$ approximations. Uniform convergence orders that are independent of the diffusion coefficient ratio inside and outside of the interface are obtained. The symmetric DDG method is shown to be capable to handle interface problems with complicated geometries.