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 …

Incompressible flow problems appear in many models of physical processes and
applications. Their numerical simulation requires in particular a spatial discretization. Finite …

Contact mechanics has its application in many engineering problems. No one can walk
without frictional contact, and no car would move for the same reason. Hence contact …

We present a survey of the fundamentals and the applications of sparse grids, with a focus
on the solution of partial differential equations (PDEs). The sparse grid approach, introduced …

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a
posteriori error estimation for linear functional outputs of affinely parametrized elliptic …

In this paper we propose a method for the finite element solution of elliptic interface problem,
using an approach due to Nitsche. The method allows for discontinuities, internal to the …

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 …

The finite element method has always been a mainstay for solving engineering problems
numerically. The most recent developments in the field clearly indicate that its future lies in …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …