A second order linear scalar diierential equation including a zero-th order term is approximated using rst the standard Galerkin method enriched with bubble functions. Static condensation of the bubbles suggest an unusual stabilized nite element method for which we establish a convergence study and obtain successful numerical simulations. The method is generalized to allow for a convection oper...

An efficient direct parallel elliptic solver based on the spectral element discretization is developed. The direct solver is based on a matrix decomposition approach which reduces multi-dimensional separable problems to a sequence of onedimensional problems that can be efficiently handled by a static condensation process. Thanks to the spectral accuracy and the localized nature of a spectral el...

Based on both static (extended Köhler) and dynamic modelling, we investigate the influence of temperature, humidity, HNO(3) initial concentration, as well as of the particle concentration, on the efficiency of HNO(3)-mediated laser-induced condensation. This mechanism is most efficient for low temperatures, high HNO(3) concentration, and relative humidities. It is, however, still active up to 3...

Self-tuning control with recursive identification of extremal dynamic systems is considered. The systems can be represented by combinations of linear dynamic and extremal static parts, their output being disturbed by a coloured noise. Minimumvariance controllers for Hammerstein, Wiener, and Wiener-Hammerstein-type systems are designed taking into consideration restrictions for control signal ma...

A component-based approach is introduced for fast and flexible solution of parameter-dependent eigenproblems. We consider a shifted version of the eigenproblem where the left hand side operator corresponds to an equilibrium between the stiffness operator and a weighted mass operator. This permits to apply the Static Condensation Reduced Basis Element method, a domain synthesis approach with red...

Abstract. In this paper we perform an error analysis for a multiscale finite element method for singularly perturbed reaction–diffusion equation. Such method is based on enriching the usual piecewise linear finite element trial spaces with local solutions of the original problem, but do not require these functions to vanish on each element edge. Bubbles are the choice for the test functions all...

A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov-Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions ...

A second order linear scalar diierential equation including a zero-th order term is approximated using rst the standard Galerkin method enriched with bubble functions. Static condensation of the bubbles suggest an unusual stabilized nite element method for which we establish a convergence study and obtain successful numerical simulations. The method is generalized to allow for a convection oper...

In this work we propose an adaptive version of the recently introduced Mixed High-Order method and showcase its performance on a comprehensive set of academic and industrial problems in computational electromagnetism. The latter include, in particular, the numerical modeling of comb-drive and MEMS devices. Mesh adaptation is driven by newly derived, residual-based error estimators. The resultin...

We investigate the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one and two component, two phase fluids. In this, the first of two papers, we consider liquid-gas systems. Careful implementation of the thermodynamic boundary condition allows us to fix the static contact angle in the simulations. We then consider the behav...