关键词: 杂交混合有限元方法, 间断系数, 椭圆方程, 界面问题, L a g r a n g e乘子

Abstract: This paper discusses the hybrid mixed finite element method for elliptic interface problem in which the solution and gradient are discontinuous because of jump conditions across the interface. For the twodimensional elliptic interface problem, we propose the hybrid mixed finite element method on triangulation. The properties of this method mainly reflect in the following: the triangular mesh can nicely approximate the complex interface|they provide the approximations of all the variables, including the solution and gradient, with the optimal order|the matrix of final linear algebra systems is symmetric and positive definite, so it can be numerically solved by using for example conjugate gradient method. Numerical examples demonstrate the validity of hybrid mixed finite element method for elliptic interface problems. 

Key words: Hybrid mixed finite element method, Discontinuous coefficient, Elliptic equation, Interface problem, Lagrange multipliers