XHDG Method For Solving 2-D Elliptic Interface Problems

In this thesis,a new numerical method based on hybridizable discontin-uous Galerkin(HDG)method is developed for solving 2-D elliptic interface problem.Two important features of this method are as follows.First,it uses quasi-uniform mesh without fitting the interface.Second,it has second order convergence.We focus on the interface problem with discontinuous coefficien-t.The interface problem is firstly transfer to a extended interface problem by introduce a piece-wise polynomial ansatz function in the vicinity of the int.er-face.In the extended interface problem,the interface is fitted with a given quasi-uniform mesh.Then HDG method is adopted to solve the extended in-terface problem.By changing the numerical flux,the jump conditions can be naturally incorporated into the numerical scheme.The ansatz function ua.,h depends on the unknown function u.We use the values of u at some control points on the interface to determine ua,h.Therefore,ua,h needs to be solved out together with u.We use three different interface to validate the feasibility of the method.The numerical results also show that the proposed method has second order convergence rates in both L2 and L? norm.