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Oberseminar Numerische Mathematik / Scientific Computing

 

Christoph Schwab

ETH Zürich

Deterministic Approximations of Elliptic PDEs with Stochastic Coefficients

Abstract:

We present a deterministic FEM for the solution of elliptic problems with stochastic coefficients which are given as spatially inohomogeneous random fields.

It is based on various expansions (such as, e.g., Karhunen Loeve) of the input data and on a spectral approximation of `Polynomial Chaos' type in the sense of N. Wiener of the joint probability densities of the random solution.

Numerical analysis of the random solution's regularity are presented and used in an algorithm for the efficient computation of the solution, which exploits the hierarchic nature of the polynomial approximations in the probability domain and of the multilevel discretization in the physical domain.

Estimates of convergence rates and of the complexity of the method are given.

Joint work M. Bieri of ETH and A. Cohen (Paris VI, France) and R. A. DeVore (Texas A&M, USA).

Datum: 04.11.09
Zeit:16:00 Uhr
Ort:Zuse Institut Berlin, Takustr. 7, 14195 Berlin.
Raum:Seminarraum im Erdgeschoss

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