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Adaptive stochastic Galerkin methods: beyond the elliptic case

by C. J. Gittelson

(Report number 2011-12)

Abstract
We derive an adaptive solver for random boundary value problems, building on adaptive wavelet algorithms for non-elliptic problems. Replacing wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence, which may be combined with any discretization on the spatial domain. We show optimality properties of this solver, and present numerical computations, including a comparison of various adaptive methods.

Keywords:

@Techreport{G11_116,
  author = {C. J. Gittelson},
  title = {Adaptive stochastic Galerkin methods: beyond the elliptic case},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-12.pdf },
  year = {2011}
}

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