The solution of non‐linear hyperbolic equation systems by the finite element method

The difficulties experienced in the treatment of hyperbolic systems of equations by the finite element method (or other) spatial discretization procedures are well known. In this paper a temporal discretization precedes the spatial one which in principle is considered along the characteristics to achieve a self adjoint form. By a suitable expansion, the original co‐ordinates are preserved and combined with the use of a standard Galerkin process to achieve an accurate discretization. It is shown that the process is equivalent to the Taylor‐Galerkin methods of Donea.17 Several examples illustrate the accuracy and efficiency attainable in such problems as transport, shallow water equations, transonic flow etc.