Superconvergence of bi-$k$ Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations

Abstract

In this paper, we present a superconvergence result for the bi-$k$ degree time-space fully discontinuous finite element of first-order hyperbolic problems. Based on the element orthogonality analysis (EOA), we first obtain the optimal convergence order of discontinuous Galerkin finite element solution. Then we use orthogonality correction technique to prove a superconvergence result at right Radau points, which is one order higher than the optimal convergence rate. Finally, numerical results are presented to illustrate the theoretical analysis.