A Split Least-Squares Characteristic Mixed Finite Element Method for the Convection Dominated Sobolev Equations

Abstract

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L 2 and H 1 normed spaces for the primal unknown and with the optimal order in L 2 normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.