Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Mixed hp-DGFEM for Incompressible Flows
SIAM Journal on Numerical Analysis
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Space-time discontinuous Galerkin method for nonlinear water waves
Journal of Computational Physics
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
A space--time discontinuous Galerkin method for the time-dependent Oseen equations
Applied Numerical Mathematics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
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This article presents a space-time discontinuous Galerkin (DG) finite element discretization of the advection-diffusion equation on time-dependent domains. In the space-time DG discretization no distinction is made between the space and time variables and discontinuous basis functions are used both in space and time. This approach results in an efficient numerical technique for physical applications which require moving and deforming elements, is suitable for hp-adaptation and results in a fully conservative discretization. A complete derivation of the space-time DG method for the advection-diffusion equation is given, together with the relation of the space-time discretization with the arbitrary Lagrangian Eulerian (ALE) approach. Detailed proofs of stability and error estimates are also provided. The space-time DG method is demonstrated with numerical experiments that agree well with the error analysis.