Considerable advances in numerical methods for partial differential equations have been achieved since Harry Yserentant wrote his Habilitation thesis in 1984. Starting from meanwhile classical multi-grid methods and domain decomposition,  subspace correction approaches have revolutionized the efficient solution of  partial differential equations. Sparse grids and hierarchical tensor approximations have paved the way towards the efficient solution of high-dimensional elliptic problems with sufficient regularity, like the electronic Schrödinger equation, and extensions to various nonlinear problems are under way.

The aim of this workshop is to review these developments, to highlight some hot topics of current research and to discuss future perspectives.