Explicit Finite Element Methods for Symmetric Hyperbolic Equations

Abstract

A family of explicit space-time finite element methods for the initial boundary value problem for linear, symmetric hyperbolic systems of equations is described and analyzed. The method generalizes the discontinuous Galerkin method and, as is typical for this method, obtains error estimates of order $O(h^{n+1/2})$ for approximations by polynomials of degree $\le n$.