The main focus of my current research is the approximation of high-dimensional functions and the solution of partial differential equations in high dimensions. A central tool in this respect is the dimension-adaptive sparse grid method and its generalizations. Another focus is the development of efficient numerical methods for the treatment of flow problems and for the simulation of materials on the atomistic and the continuous scale. Finally, adaptive finite element discretizations, multi-level solvers of the arising linear systems and their parallelization are investigated.