The Time Discontinuous Galerkin TSFE Method For Hyperbolic Equations

The viscoelastic equation and Sine-Gordon equation are two kinds of hyperbolic partial differential equations,which widely used in many fields such as fluid mechanics According to the characteristics of the equation,firstly,the auxiliary variable ?=ut is introduced to transform the original problem into a system of reduced order equa-tions in this paper.Then,the time-discontinuous space-time finite element scheme is constructed to solve the approximate solutions of displacement u and velocity ut.The stability of the scheme is proved by combining the finite element analysis with the La-grange interpolation which takes the Radau integral point as the node,and the optimal error estimation of displacement u in the L?([0,T];H1(?))-norm and velocity ?=utin the L?([0,T];L2(?))-norm is also proved by this method.Finally,the correctness of the theoretical results of error estimation is verified by a numerical example.