Preliminary list of abstracts

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Convergence rates of a sparse tensor QMC-FEM discretizations for a class of PDEs with infinite dimensional noise
Keywords: Stochastic PDEs; Multilevel QMC
Tue, 09:25--09:50
  • Schwab, Christoph (Mathematics, ETH Zurich, Switzerland)
  • Kuo, Frances Y. (Department of Mathematics, Univ. New South Wales, Australia)
  • Sloan, Ian H. (Department of Mathematics, Univ. New South Wales, Australia)

We consider elliptic partial differential equations with infinite dimensional noise in the coefficients.

We present an analysis of the PDE to establish new sufficient conditions on the random inputs' fluctuations in order for several families of QMC rules to converge at rates independent of the dimension of the noise.

We present convergence rates of sparse tensor discretizations by QMC methods in random space and by Finite Element Methods in physical space and time.

Extensions to parabolic and hyperbolic PDEs will be indicated.

The results presented here are joint work with Frances Kuo and Ian Sloan. They are building on a new unification of several error bounds for QMC quadratures which are presented in a related talk by I. Sloan.