Introduction 23 1. Abstract minimization problems, variational inequalities and the Lax-
Milgram lemma 24 2. The Sobolev spaces H (Q2) and Green's formulae 30 3. Examples of …

The material covered by this book has been taught by one of the authors in a post-graduate
course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an …

The purpose of this article is to survey what is mathematically known about local behavior in
finite element projection methods. The purpose of this introductory chapter is to display …

This book is essentially a set of lecture notes from a graduate seminar given at Cornell in
Spring 1994. It treats basic mathematical theory for superconvergence in the context of …

The stability of the ${L_2} $-projection onto some standard finite element spaces ${V_h} $,
considered as a map in ${L_p} $ and $ W_p^ 1$, $1\leqslant p\leqslant\infty $, is shown …

Flow in fractured porous media represents a challenge for discretization methods due to the
disparate scales and complex geometry. Herein we propose a new discretization, based on …

The objective of this paper is to introduce a general scheme for deriving a posteriori error
estimates by using duality theory of the calculus of variations. We consider variational …

We study the numerical approximation of boundary optimal control problems governed by
semilinear elliptic partial differential equations with pointwise constraints on the control. The …

We consider an elliptic optimal control problem with pointwise state constraints. The cost
functional is approximated by a sequence of functionals which are obtained by discretizing …

For a model convection-dominated singularly perturbed convection-diffusion problem, it is
shown that crosswind smear in the numerical streamline diffusion finite element method is …