Sharp L2-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media

Sharp L-error Estimates and Superconvergence of Mixed Finite Element Methods for Non-fickian Flows in Porous Media∗

Abstract. A sharper L-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz–Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75–84]. Moreover, local L superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points ...

L1-error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for Nonfickian Flows in Porous Media

Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids

We establish interior velocity superconvergence estimates for mixed finite element approximations of second order elliptic problems on non-matching rectangular and quadrilateral grids. Both mortar and non-mortar methods for imposing the interface conditions are considered. In both cases it is shown that a discrete L2-error in the velocity in a compactly contained subdomain away from the interfa...

Superconvergence of mixed finite element methods for optimal control problems

In this paper, we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods. The state and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Some realistic regularity a...

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...