A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains

Abstract

In this manuscript, we consider an efficient dissipation-preserving finite element method for a class of two-dimensional nonlinear fractional wave equations on irregular convex domains. We show that the fully discrete method preserves the discrete energy structures under the same boundary conditions as the continuous model. Furthermore, the optimal order error estimates of the fully discrete scheme are proved in detail. Finally, the numerical simulations, which are based on spatial unstructured meshes, are presented to confirm the correctness of the theoretical results.