High order DG-DGLM method for hyperbolic conservation laws

A high order discontinuous Galerkin method in time combined with discontinuous Galerkin method with Lagrange multiplier (DGLM) (Kim, 2015) [4] in space is proposed to approximate the solution to hyperbolic conservation laws with boundary conditions. Stability of the approximate solution is proved in a broken L2(L2) norm and also in an l∞(L2) norm. Error estimates of O(hr+12+knq+12) with Pr(E) and Pq(Jn) elements (r,q≥d+12) are 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. An explanation on algorithmic aspects is given.