This article surveys a general approach to error control and adaptive mesh design in
Galerkin finite element methods that is based on duality principles as used in optimal …

Error estimation and control are critical ingredients for improving the reliability of
computational simulations. Adjoint-based techniques can be used to both estimate the error …

These Lecture Notes have been compiled from the material presented by the second author
in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH …

We give an overview of recent developments concerning the use of adjoint methods in two
areas: the a posteriori error analysis of finite element methods for the numerical solution of …

In this paper we review the basic concepts to obtain a posteriori error estimates for the finite
element solution of an elliptic linear model problem. We give the basic ideas to establish …

An anisotropic, unstructured grid adaptive method is presented for improving the accuracy of
functional outputs of viscous, compressible flow simulations for general discretizations. The …

Motivated by applications in computational fluid dynamics, a method is presented for
obtaining estimates of integral functionals, such as lift or drag, that have twice the order of …

I am an old man now, and when I die and go to heaven there are two matters on which I
hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent …

These notes are based on lectures given in a Short Course on Theoretical and Numerical
Fluid Mechanics in Vancouver, British Columbia, Canada, July 27–28, 1996, and at several …

In this paper, we derive a posteriori error estimates for the finite element approximation of
distributed optimal control problems governed by the Stokes equations. We obtain a …