Superconvergence in Some Locally Conservative Discretization Methods

Thursday, May 13, 2004 - 9:30am - 10:20am
Keller 3-180
Ivan Yotov (University of Pittsburgh)
Mixed finite element methods (MFEM), control-volume mixed finite element methods (CVMFEM), and mimetic finite difference methods (MFDM) are locally mass conservative discretization methods that perform well on diffusion-type problems with rough grids and coefficients. All methods provide accurate approximations of both the scalar variable (pressure) and its flux (velocity). Each method has advantages and disadvantages, which will be discussed. MFEM are naturally formulated as variational methods. CVMFEM were originally developed as finite volume methods, while MFDM are based on discrete operators that preserve critical properties of the differential operators. More recently, CVMFEM and MFDM have been formulated as variational methods and shown to be related to MFEM. We discuss how these relationships can be employed to establish superconvergence for CVMFEM and MFDM in both pressure and velocity. Extensions of these results to mortar discretizations on non-matching grids will also be discussed.

This talk reports on joint work with Markus Berndt, Konstantin Lipnikov, and Misha Shashkov, LANL, Tom Russell, University of Colorado Denver, and Mary Wheeler, University of Texas at Austin.