Local flux conservative numerical methods for the second order elliptic equations

A discontinuous Galerkin type nonconforming element method and a local flux matching nonconforming element method for the second order elliptic boundary value problems are presented. Both of these methods enjoy the local flux conservation property. The local flux matching method finds a numerical solution in the same solution space of the DG type nonconforming element method, but it achieves much faster iterative convergence speed by embedding continuity requirement in the approximation functions rather than using constraint equations that are used in the DG type nonconforming element method. The merits of the proposed local flux matching method are as follows: the formulation of the method is simple and the solution satisfies local flux conservation property. Moreover, it can be easily applied to general elliptic equations.