The local discontinuous Galerkin method with generalized alternating flux applied to the second-order wave equations (Q2205916)

Summary: In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional second-order wave equation with the periodic boundary conditions. Introducing two auxiliary variables, the second-order equation is rewritten into the first-order equation systems. We prove the stability and energy conservation of this method. By virtue of the generalized Gauss-Radau projection, we can obtain the optimal convergence order in \(L^2\)-norm of \(\mathcal{O} (h^{k+1})\) with polynomial of degree \(k\) and grid size \(h\). Numerical experiments are given to verify the theoretical results.