Superconvergence of bi-$k$ Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we present a superconvergence result for the bi-$k$ degree time-spacefully discontinuous finite element of first-order hyperbolic problems. Based onthe element orthogonality analysis (EOA), we first obtain the optimal convergence orderof discontinuous Galerkin finite element solution. Then we use orthogonality correctiontechnique to prove a superconvergence result at right Radau points, which is one order higher than the optimal convergence rate. Finally, numerical results are presentedto illustrate the theoretical analysis.