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hp-FEM for second moments of elliptic PDEs with stochastic data Part 2: Exponential convergence

by B. Pentenrieder and Ch. Schwab

(Report number 2010-09)

Abstract
We prove exponential rates of convergence of a class of hp Galerkin Finite Element approximations of solutions to a model tensor non-hypoelliptic equation in the unit square _ = (0,1)2 which exhibit singularities on@_ and on the diagonal _ = ((x,y)2_:x=y), but are otherwise analytic in _. As we explained in the first part [6] of this work, such problems arise as deterministic second moment equations of linear, second order elliptic operator equations Au = f with Gaussian random field data f.

Keywords:

@Techreport{PS10_73,
  author = {B. Pentenrieder and Ch. Schwab},
  title = {hp-FEM for second moments of elliptic PDEs with stochastic data Part 2: Exponential convergence},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-09.pdf },
  year = {2010}
}

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