The Stabilized Time Discontinuous Galerkin Space-Time Finite Element Methods For Two Kinds Of Equations

A kind of stabilized time discontinuous space-time finite element formulations is presented for convection equations and convection-reaction-diffusion equations.The sta-bilized schemes considered in this paper are constructed based on the streamline upwind finite element approximate scheme,combining with the space-time finite element method in which the discrete time variation form is used.The theoretical proofs of the scheme cannot be found in relative references,although there are some simulations in practical applications.In this paper,we give the proofs of stability and error estimates in the maximum norm of time and L~2(?)-norm of spacial by taking the Radau points as the interpolation nodes of Lagrange interpolation polynomials.The temporal and spacial variables are decoupled,and the restricted conditions on the space-time meshes are re-moved by taking advantages of the techniques of combining the interpolation polynomials with the finite element method.The process of proofs in this paper provides a new idea of theoretical analysis for the stabilized space-time finite element method permitting dis-continuities in time.And the complexities in practical computations caused by unifying space and time variables are conquered.