Matrix Oriented Reduction of Space-Time Petrov-Galerkin Variational Problems

Space-time least-squares Petrov-Galerkin projection for nonlinear model reduction

This work proposes a space–time least-squares Petrov–Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov– )Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed me...

Stability of Petrov-Galerkin Discretizations: Application to the Space-Time Weak Formulation for Parabolic Evolution Problems

This paper is concerned with the stability of Petrov-Galerkin discretizations with application to parabolic evolution problems in space-time weak form. We will prove that the discrete inf-sup condition for an a priori fixed Petrov-Galerkin discretization is satisfied uniformly under standard approximation and smoothness conditions without any further coupling between the discrete trialand test ...

Meshless Local Petrov-Galerkin (MLPG) Method for Convection-Diffusion Problems

Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multidimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convectiondiffusion problems, in one and two dimensions. Even fo...

A-stable discontinuous Galerkin-Petrov time discretization of higher order

A Discontinuous Petrov-Galerkin Methodology for Incompressible Flow Problems