A new error analysis and post-processing technique of the lowest-order Raviart–Thomas mixed finite element method for parabolic problems

We consider error estimates and post-processing technique of the lowest order Raviart–Thomas mixed finite element method for parabolic problems. A super-convergence of the original unknown and flux is established, which is based on negative norm error estimates. At given time step, we introduce an auxiliary elliptic problem and propose a recovery strategy to obtain one-order higher finite element solutions. Corresponding results are well-known for Lagrange finite element methods for parabolic equations. By using discrete functional analysis tools developed for Discontinuous Galerkin finite element methods, we extend the analyses to the lowest order Raviart–Thomas mixed method and prove second order accuracy of the recovered numerical solutions rigorously. The proposed post-processing technique is suitable on general meshes for both two and three dimensional problems. Numerical results are provided to verify our theoretical analysis and demonstrate the efficiency of the proposed recovery methods.