Galerkin methods for the time dependent incompressible elasticity equations

Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations

Article history: Received 20 May 2015 Received in revised form 5 August 2015 Accepted 18 August 2015 Available online 10 September 2015

Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow

The main purpose of this paper is to study the stability and error estimates of the local discontinuous Galerkin (LDG) methods coupled with multi-step implicit-explicit (IMEX) time discretization schemes, for solving time-dependent incompressible fluid flows. We will give theoretical analysis for the Oseen equation, and assess the performance of the schemes for incompressible Navier-Stokes equa...

Discontinuous Galerkin methods for nonlinear elasticity

Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries

A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D geometries with the help of a continuous approximation of the electromagnetic field. In this paper, we investigate how their framework can be adapted to compute the solution to the time-dependent Maxwell equations. In addition, we propose some exten...

Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations

Two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes: (i) a discrete counterpart of the continuous Sobolev embeddings, in both Hilbertian and non-Hilbertian settings; (ii) a compactness result for bounded sequences in a suitable Discontinuous Galerkin norm, together with a weak convergence property for some discrete gradients. The...