An explicit weak Galerkin method for solving the first order hyperbolic systems

Abstract

In this paper, we present and analyze a space–time weak Galerkin finite element (WG) method for solving the time-dependent symmetric hyperbolic systems. By introducing the discrete weakly differential operator, we construct a stable WG scheme which may be in the local or global form. The local scheme can be solved explicitly, element by element, under certain mesh condition. Then, we establish the stability and derive the optimal L2-error estimate of O(hk+12)-order for the WG solution when the k-order polynomials are used for k≥0. Numerical examples are provided to show the effectiveness of the proposed WG method.