Analysis And Application Of The Expanded Mixed Finite Element Method For Two Kinds Of Evolution Equations

In this paper, we consider the Expanded Mixed Finite Element Method for the 2nd quasilinear parabolic problem and the 2nd quasilinear hyperbolic problem. This method expands the standard mixed formulation in the sense that three variable are explicitly treated: the scalar unknwon, its gradient and its flux. Optimal order error estimates for the scalar unknwon, its gradient and its flux in L2-norms are obtained for this new mixed formulation.In Chapter one, we consider the Expanded Mixed Finite Element Method for the followling 2nd order parabolic problemIn this chapter ,we propose the expanded mixed formulation for the parabolic problem, and prove that the discrete formulation has a unique solution. Optimal order error estimates for the scalar unknwon, its gradient and its flux in L2-norms are obtained.In Chapter two, we consider the Expanded Mixed Finite Element Method for the followling 2nd order hyperbolic problemIn this chapter ,we propose the expanded mixed formulation for the hyperbolic problem,and prove that the discrete formulation has a unique solution. Optimal order error estimates for the scalar unknwon, its gradient and its flux in Z-norms are obtained. In Chapter three,we present numerical results for the problem...