Sparse finite elements for stochastic elliptic problems: higher order moments

Authors:
Ch. Schwab;Radu Alexandru Todor
Affiliations:
Seminar for Applied Mathematics ETHZ, Rämistrasse 101, CH-8092 Zürich, Switzerland;Seminar for Applied Mathematics ETHZ, Rämistrasse 101, CH-8092 Zürich, Switzerland
Venue:
Computing
Year:
2003

Citing 4
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Abstract

We define the higher order moments associated to the stochastic solution of an elliptic BVP in D ⊂ Rd with stochastic input data. We prove that the k-th moment solves a deterministic problem in Dk ⊂ Rdk, for which we discuss well-posedness and regularity. We discretize the deterministic k-th moment problem using sparse grids and, exploiting a spline wavelet basis, we propose an efficient algorithm, of logarithmic-linear complexity, for solving the resulting system.