An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations

09/09/2021
by   Qi Tao, et al.
0

In this paper, we develop an oscillation free local discontinuous Galerkin (OFLDG) method for solving nonlinear degenerate parabolic equations. Following the idea of our recent work [J. Lu, Y. Liu, and C.-W. Shu, SIAM J. Numer. Anal. 59(2021), pp. 1299-1324.], we add the damping terms to the LDG scheme to control the spurious oscillations when solutions have a large gradient. The L^2-stability and optimal priori error estimates for the semi-discrete scheme are established. The numerical experiments demonstrate that the proposed method maintains the high-order accuracy and controls the spurious oscillations well.

READ FULL TEXT
09/15/2021

A discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations

This paper proposes and analyzes an ultra-weak local discontinuous Galer...
11/28/2020

High order asymptotic preserving discontinuous Galerkin methods for gray radiative transfer equations

In this paper, we will develop a class of high order asymptotic preservi...
09/05/2020

Linearized Continuous Galerkin hp-FEM Applied to Nonlinear Initial Value Problems

In this note we consider the continuous Galerkin time stepping method of...
09/06/2021

A well-balanced oscillation-free discontinuous Galerkin method for shallow water equations

In this paper, we develop a well-balanced oscillation-free discontinuous...
07/03/2020

An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations

This paper develops a high order adaptive scheme for solving nonlinear S...
10/08/2021

Local discontinuous Galerkin methods for the abcd nonlinear Boussinesq system

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