Abstract
An arbitrary order discontinuous Galerkin method in space and time is proposed to approximate the solution to hyperbolic systems of multi-dimensional conservation laws. Weak formulation is derived through the definition of weak divergence. Weak solution is given as a pair of weak functions on the element and the edge, respectively. Weak solution on the edge is characterized as the average of the solutions on the elements sharing the edge. Stability of the approximate solution is proved in a broken L2(L2) norm and also in a broken l∞(L2) norm. Error estimates of O(hr+knq) with Pr(E) and Pq(Jn) elements (r,q>1+d2) are then derived in a broken L2(L2) norm, where h and kn are the maximum diameters of the elements and the time step of Jn, respectively, Jn is the time interval, and d is the dimension of the spatial domain.
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