Structure-Preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/hp Element Methods

Discontinuous Galerkin methods for nonlinear elasticity

Parallel Iterative Discontinuous Galerkin Finite-element Methods

We compare an iterative asynchronous parallel algorithm for the solution of partial diierential equations, with a synchronous algorithm , in terms of termination detection schemes and performance. Both algorithms are based on discontinuous Galerkin nite-element methods, in which the local elements provide a natural decomposition of the problem into computationally-independent sets. We demonstra...

Mass preserving discontinuous Galerkin methods for Schrödinger equations

Article history: Received 19 January 2014 Received in revised form 13 October 2014 Accepted 12 November 2014 Available online 18 November 2014

Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics

In this paper, we develop discontinuous Galerkin (DG) methods to solve ideal special relativistic hydrodynamics (RHD). In RHD, the density and pressure are positive. Units are normalized so that the speed of light is c = 1. Therefore, the velocity of the fluid has magnitude less than 1. To construct physically relevant numerical approximations, we develop a bound-preserving limiter to the schem...

Coupling Methods for Interior Penalty Discontinuous Galerkin Finite Element Methods and Boundary Element Methods

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element meth...