SUPERCONVERGENCE ERROR ESTIMATES OF THE LOWEST-ORDER RAVIART-THOMAS GALERKIN MIXED FINITE ELEMENT METHOD FOR NONLINEAR THERMISTOR EQUATIONS

This paper is concerned with the superconvergence error estimates of a classical mixed finite element method for a nonlinear parabolic/elliptic coupled thermistor equations. The method is based on a popular combination of the lowest-order rectangular Raviart-Thomas mixed approximation for the electric potential/field ( phi, theta ) and the bilinear Lagrange approximation for temperature u. In terms of the special properties of these elements above, the superclose error estimates with order O ( h 2 ) are obtained firstly for all three components in such a strongly coupled system. Subsequently, the global superconvergence error estimates with order O ( h 2 ) are derived through a simple and effective interpolation post-processing technique. As by a product, optimal error estimates are acquired for potential/field and temperature in the order of O ( h) and O ( h 2 ), respectively. Finally, some numerical results are provided to confirm the theoretical analysis.