A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes
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Date
2014-01Type
- Report
ETH Bibliography
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Abstract
We analyze a-posteriori error estimation and adaptive refinement algorithms for stochastic Galerkin Finite Element methods for countablyparametric, elliptic boundary value problems. A residual error estimator which separates the effects of gpc-Galerkin discretization in parameter space and of the Finite Element discretization in physical space in energy norm is established. It is proved that the adaptive algorithm converges, and to this end we establish a contraction property satisfied by its iterates. It is shown that the sequences of triangulations which are produced by the algorithm in the FE discretization of the active gpc coefficients are asymptotically optimal. Numerical experiments illustrate the theoretical results. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010386302Publication status
publishedJournal / series
Research ReportVolume
Publisher
ETH ZürichSubject
GALERKIN METHOD (NUMERICAL MATHEMATICS); Uncertainty quantification; Residual a-posteriori error estimation; ELLIPTISCHE DIFFERENTIALGLEICHUNGEN (ANALYSIS); MEHRGITTERVERFAHREN + GITTERERZEUGUNG (NUMERISCHE MATHEMATIK); Generalized polynomial chaos; PARTIELLE DIFFERENTIALGLEICHUNGEN HÖHERER ORDNUNG (NUMERISCHE MATHEMATIK); PARTIAL DIFFERENTIAL EQUATIONS OF HIGHER ORDER (NUMERICAL MATHEMATICS); GALERKIN-VERFAHREN (NUMERISCHE MATHEMATIK); FINITE-ELEMENTE-METHODE (NUMERISCHE MATHEMATIK); FINITE ELEMENT METHOD (NUMERICAL MATHEMATICS); Adaptive Finite Element Methods; Contraction property; ELLIPTIC DIFFERENTIAL EQUATIONS (MATHEMATICAL ANALYSIS); MULTIGRID METHODS + GRID GENERATION (NUMERICAL MATHEMATICS)Organisational unit
03435 - Schwab, Christoph / Schwab, Christoph
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
Funding
247277 - Automated Urban Parking and Driving (EC)
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ETH Bibliography
yes
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