Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations (Communications in Computational Physics, 2021)
In this paper, we construct high order energy dissipative and conservativelocal discontinuous Galerkin methods for the Fornberg-Whitham type equations. Wegive the proofs for the dissipation and conservation for related conservative quantities. The corresponding error estimates are proved for the proposed schemes. Thecapability of our schemes for different types of solutions is shown via several numerical experiments. The dissipative schemes have good behavior for shock solutions,while for a long time approximation, the conservative schemes can reduce the shapeerror and the decay of amplitude significantly.