Analytical and Numerical Developments in Optimal Shape Design for Aerospace: An overview

Analysis of finite element methods for coupled Hydro-Mechanical problems

This work is concerned with the analysis of a non-stationary Hydro-Mechanical problem. The well-posedness of the continuous, time semi-discretized and fully discretized problems is addressed. An a posteriori error analysis is performed, leading to a family of space-time error indicators. The reliability of this family, i.e. a global upper bound...

A parallel finite element method for two-phase flows

A parallel finite element model for incompressible laminar two-phase flows is presented. A two-fluid model, describing the laminar non-equilibrium flow of two incompressible phases, is discretized by means of a properly designed Streamline Upwind Petrov-Galerkin (SUPG) finite element procedure. Such a procedure is consistent with a continuous...

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...

Space-Time Discontinuous Galerkin Method for the Compressible Navier-Stokes

An overview is given of a space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations. This method is well suited for problems with moving (free) boundaries which require the use of deforming elements. In addition, due to the local discretization, the space-time discontinuous Galerkin method is well...

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...