Enhanced velocity mixed finite element methods for flow in multiblock domains

Mary F. Wheeler TICAM, Department of Aerospace Engineering \& Engineering Mechanics, and Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712; mfw@ticam.utexas.edu


A new approach to modeling flow in porous media via mixed finite element methods on non-matching multiblock grids is presented. The method is somewhat simpler and less expensive than the mortar method, since flux continuity is incorporated in the velocity space. Theoretical a priori estimates and numerical studies for single-phase flow show almost optimal convergence for pressure and interior velocity. Computational results for two-phase flow indicate that the enhanced velocity method provides accuracy comparable to the mortar method at substantially reduced cost. This work is joint with John Wheeler and Ivan Yotov.