The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic fail. Our analysis covers two- and three-dimensional domains, conforming non-conforming as well different elements. This variety of settings requires approaches results in estimators. Furthermore many examples pairs that are covered by presented. Lower upper bounds form main result...

In finite element computations, the choice of mesh is crucial to obtain accurate solutions. order evaluate quality mesh, a posteriori error estimators can be used. this paper, we develop residual-based for magnetostatic problems with both classical formulations in term potentials used, as well equilibrated estimator. We compare their behaviors on some numerical applications, understand interest each them remeshing process.

Abstract In this work, we propose an a posteriori goal-oriented error estimator for the harmonic $\textbf {A}$-$\varphi $ formulation arising in modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on resolution adjoint problem associated with initial one. For each these two guaranteed equilibrated developed using some flux reconstructions. These fluxes also allow to obtain that fully computable and can be split principal part remainder Our...

This paper is devoted to the derivation of an a posteriori residual-based error estimator for A-φ magnetodynamic harmonic formulation Maxwell system. The weak continuous and discrete formulations are established, well-posedness both them addressed. Some useful analytical tools derived. Among them, ad hoc Helmholtz decomposition proven, which allows pertinently split error. Consequently, obtained, proven be reliable locally efficient. Finally, numerical tests confirm theoretical results.

Ahmed body with a 25° rear window is used to represent simplified car geometry. Two- and three-dimensional simulations are performed analyse the flow behaviour around such vehicle. Sucking blowing jets or slots added on control flow. The results presented show that good drag reductions achieved for choice of active procedure.

The aim of this work is to control the flow around ground vehicles by active or/and passive strategies.The achieved steady, pulsed or closed-loop jets located at backof simplified car model.The performed using porous layers between solid body and fluid in order modify shear forces.The two previous methods can be coupled improve drag reduction.

from teaching and research institutions in France or abroad, public private centers.L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques niveau recherche, publiés ou non, émanant des établissements d'enseignement recherche français étrangers, laboratoires publics privés.A guaranteed equilibrated error estimator for the A -φ T -Ω magnetodynamic harmonic formulations of Maxwell system

Summary In this paper, we consider some potential formulations of electrostatic as well time‐harmonic eddy current problems with voltage or excitation sources. The well‐posedness each formulation is first established. Then, the reliability corresponding residual‐based a posteriori estimators derived in context finite element method approximation. Finally, implementation an industrial code performed, and obtained theoretical results are illustrated on academic benchmark. Copyright © 2015 John...

Abstract A new artificial boundary condition for two‐dimensional subsonic flows governed by the compressible Navier–Stokes equations is derived. It based on hyperbolic part of equations, according to way propagation characteristic waves. reference flow, as well a convection velocity, used properly discretize terms corresponding entering Numerical tests various classical model problems, whose solutions are known, and comparisons with other conditions (BCs), show efficiency BC. Direct...

Abstract This article presents a posteriori error estimates for the mixed discontinuous Galerkin approximation of stationary Stokes problem. We consider anisotropic finite element discretizations, i.e., elements with very large aspect ratio. Our analysis covers two‐ and three‐dimensional domains. Lower upper bounds are proved minimal assumptions on meshes. The lower bound is uniform respect to mesh anisotropy. depends proper alignment anisotropy mesh, which common feature estimation. In...

We consider some (anisotropic and piecewise constant) convection–diffusion–reaction problems in domains of ℝ2, approximated by a discontinuous Galerkin method with polynomials any degree. propose two posteriori error estimators based on gradient recovery averaging. It is shown that these give rise to an upper bound where the constant explicitly known up additional terms guarantee reliability. The lower also established, one being robust when convection term (or reaction term) becomes...

For eddy current problems, potential formulations are widely used nowadays. In this paper, residual based a posteriori error estimators introduced to evaluate the discretization in finite element calculation both case of <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> /φ and xmlns:xlink="http://www.w3.org/1999/xlink">T</b> /Ω harmonic formulations. A device with currents is studied order show efficiency proposed estimators.