Abstract. A new residual local projection stabilized method (RELP) is proposed as a result of an enriched Petrov-Galerkin strategy for the Oseen problem. The P 1 × Pl pairs, l = 0, 1 with continuous or discontinuous pressures, are made stable by enhancing them with solutions of residual-based local Oseen problems and performing a static condensation procedure afterward. This process does not in...

This work addresses stabilized equal-order finite elements for the hydrostatic approximation of the three-dimensional (3D) Stokes equations which is also called 2.5D Stokes problem. By defining appropriate averaging operators, several stabilized schemes for the two-dimensional (2D) Stokes problem can be generalized to this 2.5D problem, as e.g. pressure stabilized Petrov-Galerkin, local project...

We offer an alternative way of evalating the relative importance of the state coordinates of a nonlinear control system. Our approach is based on making changes of state coordinates to bring the controllability and observability functions into input normal form. These changes of coordinates are done degree by degree and the resulting normal form is unique through terms of degree seven. 1 The Pr...

Model order reduction is a mathematical technique to transform nonlinear dynamical models into smaller ones, that are easier to analyze. In this paper we demonstrate how model order reduction can be applied to nonlinear electronic circuits. First we give an introduction to this important topic. For linear time-invariant systems there exist already some well-known techniques, like Truncated Bala...

Reduced-order models of the nonlinear Complex Ginzburg-Landau (CGL) equation are computed using a nonlinear generalization of balanced truncation. The method involves Galerkin projection of the nonlinear dynamics onto modes determined by balanced truncation of a linearized system, and is compared to a standard method using projection onto Proper Orthogonal Decomposition (POD) modes computed fro...

For general non-linear parametrized partial differential equations (PDEs), the standard Galerkin projection is no longer efficient to generate reduced-order models. This is because the evaluation of the integrals involving the non-linear terms has a high computational complexity and cannot be pre-computed. This situation also occurs for linear equations when the parametric dependence is nonaffi...

A primitive-variable formulation for simulation of time-dependent incompressible flows in cylindrical coordinates is developed. Spectral elements are used to discretise the meridional semi-plane, coupled with Fourier expansions in azimuth. Unlike previous formulations where special distributions of nodal points have been used in the radial direction, the current work adopts standard Gauss–Lobat...

We introduce an ultraweak space-time variational formulation for the wave equation, prove its well-posedness (even in case of minimal regularity) and optimal inf-sup stability. Then, we a tensor product-style Petrov–Galerkin discretization with discrete stability, obtained by non-standard definition trial space. As consequence, numerical approximation error is equal to residual, which particula...

We considered an hybridizable discontinuous Galerkin (HDG) method for discrete elliptic PDEs with random coefficients. By approach of projection, we obtained the error analysis under assumption that a(ω,x) is uniformly bounded. Together HDG method, applied a multilevel Monte Carlo (MLMC) (MLMC-HDG method) to simulate PDEs. derived overall convergence rate and total computation cost estimate. Fi...

Reduced-order models for plane Couette flow are obtained by Galerkin projection of the Navier-Stokes equations onto leading controllability modes linearized system. Nonlinear dynamical systems so constructed, with various degrees truncation, numerically stable and reproduce statistics minimal turbulent at Reynolds numbers 500 1200 different choices modal bases. A closure model was not included ...