Superconvergence Of Time-Space Fully Discontinuous Finite Element For Fist-Order Hyperbolic Systems

In this paper,we study the first-order hyperbolic systems by using time-space fully discontinuous finite element.Based on the element orthogonality analysis(EOA),the tensor product decompose.And the correction function is constructed on the element bar to discuss the convergence of the double k discontinuous element.In this paper,we use the modified function to deal with the main error terms,and get the first order superconvergence result on the right Radau point.In the numerical experiment part,this paper mainly discusses the case of two-dimensional and three-dimensional.By calculation and analysis,We get the error estimate of full order for the full discrete space-time discrete discontinuous finite element solution,especially the left limit of its error has superconvergence on the right Radau point of the k+1 order.The numerical results agree with the theoretical analysis.