High order DG-DGLM method for hyperbolic conservation laws

초록

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 L-2(L-2) norm and also in an l(infinity)(L-2) norm. Error estimates of O(h(r+1/2) + k(n)(q+1/2)) with P-r(E) and P-q(J(n)) elements (r, q >= d+1/2) are 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. An explanation on algorithmic aspects is given. (C) 2018 Elsevier Ltd. All rights reserved.

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