Validated continuation was introduced in [4] as means of checking that the classical continuation method applied to a Galerkin projection of a PDE provides a locally unique equilibrium to the PDE of interest. In this paper we extend the numerical technique to include a parameter that leads to better bounds on the errors associated with the Galerkin truncation. We test this method on the Swift-H...

In this paper we introducé the Local Projection P° P-Discontinuous Galerkin finite elemente method (ÂI1P ° P -scheme) for solving numencally scalar conservation laws This is an exphcit method obtained by modifying the expltcit Discontinuous Galerkin method introduced by G Chavent and G Salzano [3], via a simple local projection based on the monotomcity-preserving projections introduced by van L...

In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in [1]. By this method we aim at reducing the computational cost for the approximation of a parametrized Stokes problem on a domain partitioned into subdomains. During an offline stage, expensive but performed only once, a low-dimensional approximation space is built on each s...

A full discrete two-level postprocessing Fourier Galerkin scheme for the unsteady Navier-Stokes equations with periodic boundary conditions is proposed in this talk. By defining a new projection, the interaction between the large and small eddies is reflected by the associated space splitting to some extent. Then a weakly coupled system of the large and small eddies is obtained. Stability and e...

In automotive applications large-scale nonlinear dynamical models are utilized for hardware-in-the-loop simulations and model-based controller design. A projection-based order reduction of these models, on the one hand, yields substantial advantages in computational speed and on the other hand, simplifies the controller design procedure. In this work a mathematical-empirical approach is chosen ...

This paper considers the numerical solution of time-dependent convection-diffusion-reaction equations. We shall employ combinations of streamlineupwind Petrov–Galerkin (SUPG) and local projection stabilization (LPS) meth-ods in space with the higher order variational time discretization schemes. In particular, we consider time discretizations by discontinuous Galerkin (dG) meth-ods and continuo...

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact ni...

Reduced order models are usually derived by performing the Galerkin projection procedure, where the original equations are projected onto the space spanned by a set of approximating basis functions. For Differential Algebraic Equations this projection scheme may yield an unsolvable reduced order model. This means that a model of an electrical circuit can become ill-posed if it is reduced by the...

Abstract. The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth continuous function underlying the dis...

We present a new ODE–type method of passing to the limit with the dimension of Galerkin projection for dissipative PDEs. We apply this method to trapping regions derived by Mattingly and Sinai to give a new proof of the existence and uniqueness of solutions to Navier–Stokes equations with periodic boundary conditions on the plane.