The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations

الملخص EN

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 L2-norm of Ohk+1 with polynomial of degree k and grid size h.

Numerical experiments are given to verify the theoretical results.