Space-Time Discontinuous Finite Element Method For Convection-diffusion Equation

The finite element approximation for the partial differential equation has profound effect not only on practical applications but also in theoretic analysis. As the need of numerical simulation to practical problems, many nonstandard finite element methods were proposed, such as space-time finite element method, reforming grid finite element method, moving grid finite element method and DG method etc.. In this paper, the variational problem of the convection diffusion equation is obtained firstly. Secondly, the technique of the combination of the finite element method and finite difference method is adopted to prove the existence and uniqueness of the numerical solution without the limitation of the space-time meshes. Finally, we considered the stability of dual problems, and proved L∞(L2)-norm error estimate based on the stability estimations of dual problems.