AN H-1-GALERKIN MIXED FINITE-ELEMENT METHOD FOR PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS

In this paper, an H-1-Galerkin mixed finite element method is proposed and analyzed for parabolic partial differential equations with nonsel fadjoint elliptic parts. Compared to the standard H-1-Galerkin procedu re, C-1-continuity for the approximating finite dimensional subspaces can be relaxed for the proposed method. Moreover, it is shown that the finite element approximations have the same rates of convergence as i n the classical mixed method, but without LBB consistency condition an d quasiuniformity requirement on the finite element mesh. Finally, a b etter rate of convergence for the flux in L-2-norm is derived using a modified H-1-Galerkin mixed method in two and three space dimensions, which confirms the findings in a single space variable and also improv es upon the order of convergence of the classical mixed method under e xtra regularity assumptions on the exact solution.