An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives

Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

In this paper, we develop a high order semi-implicit time discretization method for highly nonlinear PDEs, which consist of the surface diffusion and Willmore flow of graphs, the Cahn-Hilliard equation and the Allen-Cahn/Cahn-Hilliard system. These PDEs are high order in spatial derivatives, which motivates us to develop implicit or semi-implicit time marching methods to relax the severe time s...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions

Article history: Received 13 October 2014 Received in revised form 17 January 2015 Accepted 18 February 2015 Available online 2 March 2015

Arbitrary High-order Discontinuous Galerkin Method for Electromagnetic Field Problems

In this paper, we present a time integration scheme applied to the Discontinuous Galerkin finite element method (DG-FEM, [1]) for the computation of electromagnetic fields in the interior of three-dimensional structures. This approach is also known as Arbitrary High-Order Derivative Discontinuous Galerkin (ADER-DG, [2, 3]). By this method, we reach arbitrary high accuracy not only in space but ...

A High Order Discontinuous Galerkin Method for Fluid-Structure Interaction

We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations coupled to a hyperelastic Neo-Hookean membrane model. The deforming domain is handled by introducing a continuous mapping between a fixed reference configuration and the time varying domain, and rewriting the Navier-Stokes equations as a conservation law for the independent variables in the r...