Dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations

03/26/2021
by   Qian Zhang, et al.
0

In this paper, we construct high order energy dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations. We give the proofs for the dissipation and conservation for related conservative quantities. The corresponding error estimates are proved for the proposed schemes. The capability 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 shape error and the decay of amplitude significantly

READ FULL TEXT

page 1

page 2

page 3

page 4

08/11/2019

Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation

In this paper, we develop discontinuous Galerkin (DG) methods for the Os...
11/18/2019

Entropy stable discontinuous Galerkin approximation for the Relativistic Hydrodynamic Equations

This paper presents the higher-order discontinuous Galerkin entropy stab...
07/18/2019

Discontinuous Galerkin methods for short pulse type equations via hodograph transformations

In the present paper, we consider the discontinuous Galerkin (DG) method...
11/02/2020

Three discontinuous Galerkin methods for one- and two-dimensional nonlinear Dirac equations with a scalar self-interaction

This paper develops three high-order accurate discontinuous Galerkin (DG...
04/06/2020

Conservative discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System

We propose a class of conservative discontinuous Galerkin methods for th...
02/18/2021

Some continuous and discontinuous Galerkin methods and structure preservation for incompressible flows

In this paper, we present consistent and inconsistent discontinuous Gale...
10/08/2021

Local discontinuous Galerkin methods for the abcd nonlinear Boussinesq system

Boussinesq type equations have been widely studied to model the surface ...