The Full Discrete Discontinuous Finite Element Analysis for First-Order Linear Hyperbolic Equation (Journal of Computational Mathematics, 1999)
In this paper, the full discrete discontinuous Galerkin finite element method to solve 2-dimensional first-order linear hyperbolic problem is considered. Two practical schemes, Euler scheme and Crank-Nicolson scheme, are constructed. For each of them, the stability and error estimation with optimal order approximation is established in the norm stronger than $L^2$-norm.
Keywords: Hyperbolic equation; Discontinuous F.E.M.; Euler scheme.