Residual based a posteriori error analysis for the advection-diffusion equation with anisotropic and discontinuous diffusion tensor

We present a residual a posteriori error estimate for the anisotropic advection diffusion equation with continuous or discontinuous diffusion tensor. Our numerical results show that the adapted mesh based on the residual is more refined in the region where anisotropy and heterogeneity effects create diffculties for the numerical solution.

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems required for the accurate transient modeling of systems involving electromagnetic waves in many emerging technologies. While Yees explicit, energy-conserving FDTD method is still prominent but restructed to structured grids and...

NURBS-enhanced finite element method

An improvement of the classical finite element method is proposed. It considers an exact representation of the geometry by means of the usual CAD description of the boundary with Non-Uniform Rational B-Splines (NURBS). For elements not intersecting the boundary, a standard finite element interpolation and numerical integration is used....

A Finite Element Interior Penalty Method for MHD in heterogeneous domains

The Maxwell equations in the MHD limit in heterogeneous domains composed of conducting and nonconducting regions are solved by using Lagrange finite elements and by enforcing continuities across interfaces using an interior penalty technique. The method is shown to be stable and convergent and is validated by convergence tests. It is used to...

A space-time discontinuous Galerkin finite-element discretization of the Euler equations using entropy variables

A method to numerically solve the Euler equations for fluids with general equations of state is presented. It is based on a formulation solving the conservation equations for either pressure primitive variables or entropy variables, instead of the commonly used conservation variables. We use a space-time discontinuous Galerkin finite-element...

Krylov-Subspace Preconditioners for Discontinuous Galerkin Finite Element Methods

Standard (conforming) finite element approximations of convection-dominated convection-diffusion problems often exhibit poor stability properties that manifest themselves as non-physical oscillations polluting the numerical solution. Various techniques have been proposed for the stabilisation of finite element methods (FEMs) for convection...

Flooding and drying in discontinuous Galerkin discretizations of shallow water equations

Flooding and drying in space or space-time discontinuous Galerkin (DG) discretizations provides an accurate and efficient numerical scheme. Moreover, the space-time DG method is particularly suitable for moving or deforming meshes. The shallow water equations, which can exhibit flooding and drying due to the movement of water front, are...

A high-order discontinuous Galerkin solver for 3D aerodynamic turbulent flows

This paper deals with the evaluation and validation of a recently developed parallel discontinuous Galerkin code for the numerical solution of the RANS and k-omega turbulence model equations. The main features of the code can be summarized as follows: a) high-order spatial accuracy on hybrid grids, b) fully coupled, implicit time discretization,...