Markus Bachmayr
Adaptive Methods for High Dimensional PDEs
This talk gives an overview of recent results on adaptive solvers for PDEs posed on high-dimensional domains, focusing on methods that combine low-rank tensor decompositions with sparse basis expansions of the lower-dimensional tensor components. These iterative schemes are guaranteed to converge, yield computable a posteriori error bounds, and are shown to be of near-optimal computational complexity in terms of the approximability of the solution. In the particular application to model classes of parameter-dependent diffusion problems, these complexity estimates lead to an instructive comparison of different types of tensor product approximations.