Arbitrary order DG-DGLM method for hyperbolic systems of multi-dimensional conservation laws

摘要

An arbitrary order discontinuous Galerkin method in space and time is proposed to approximate the solution to hyperbolic systems of mull-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 L-2(L-2) norm and also in a broken l(infinity)(L-2) norm. Error estimates of O(h(r) + k(n)(q)) with P-r(E) and P-q(J(n)) elements (r, q 1 + d/2) are then derived in a broken L-2(L-2) norm, where h and k(n) are the maximum diameters of the elements and the time step of J(n), respectively, J(n) is the time interval, and d is the dimension of the spatial domain.