Computer Science Department, University of Maryland
jshen@cs.UMD.EDUA new mixed finite element method on totally distorted rectangular meshes is introduced with optimal error estimates for both pressure and velocity. This new mixed discretization fits the geometric shapes of the discontinuity of the rough coefficients and domain boundaries well. This new mixed method also enables us to derive the optimal error estimates and existence and uniqueness of Thomas's mixed finite elements method on distorted rectangular grids. The Lowest order Raviart-Thomas mixed finite rectangular element method becomes a special case of both methods, when all the elements are degenerated to parallelograms.