Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.co

Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems

Convergence of a finite element method based on the dual variational formulation

summary:An "equilibrium model" with piecewise linear polynomials on triangular clements applied to the solution of a mixed boundary value problem for a second order elliptic equation is studied. The procedure is proved to be second order correct in $h$ (the maximal side in the triangulation) provided the exact solution is sufficiently smooth

Sur l'intégration numérique de l'équation de Blasius de la couche limite laminaire

peer reviewe

The numerical integration of laminar boundary layer equations

AbstractSelf-similar solutions of boundary layer equations obey non-linear differential equations, automorphic under certain continuous transformation groups. Changes of variables suggested by the theory of continuous LIE groups may reduce the problem to the integration of a first order non linear differential equation, followed by quadratures, thereby greatly simplifying computer integration.The famous Blasius equation, governing the asymptotic laminar boundary layer flow over a semi-infinite plate is presented as a typical example