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 |