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.

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