Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R2. Piecewise linear finite elements are used to approximate the control as well as the state. We prove that the error estimates are of order O(h1−1/p) for some p > 2, which is consistent with the W1−1/p,p(Γ)-regularity of the optimal control

On the approximation of the spectrum of the Stokes operator

On obtient des estimations d'erreur pour le calcul approché des valeurs propres de l'opérateur de Stokes. Ces estimations sont valables pour les versions régularisées des méthodes mixtes qui satisfont la condition uniforme de Ladyzhenskaya-Babuška-Brezzi