Expanded Mixed Finite Element Numerical Analysis For Two Kinds Of Second-Order Elliptic Problems

In this paper, we consider expanded mixed finite element numerical approxi-mation for two kinds of elliptic problems, and obtain optimal order error estimate.In Chapter one, we consider the mixed eovolume method combining with theexpanded mixed finite element method for a system of first-order partial differen-tial equation resulting from the mixed formulation of general self-adjoint ellipticproblems with a full diffusion tensor.The method is an extend of the mixed finite element method on rectanglegrids, ignore the confine of the martrix, expanded the method to generic trianglegrids and equation with small coefficient.The method use the lowest. R-T expanded mixed covolume element space,obtain optimal error estimate of approximately pressure, velocity and flux.In Chapter two, we discuss a kind of strong-nonlinear elliptic problemsWe analysis the problem with expanded mixed finite element method, it needn'thave the contradictary of the coefficient. And we prove the existance and exclusive of the expanded mixed form, then achieve the optimal error estimate of approxi-mately pressure, velocity and flux.