A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes

Autor: Elmar Zander, Christoph Schwab, Martin Eigel, Claude Jeffrey Gittelson
Rok vydání: 2015
Předmět:
Contraction property
Discretization
GALERKIN METHOD (NUMERICAL MATHEMATICS)
Generalized polynomial chaos
PARTIAL DIFFERENTIAL EQUATIONS OF HIGHER ORDER (NUMERICAL MATHEMATICS)
MULTIGRID METHODS + GRID GENERATION (NUMERICAL MATHEMATICS)
FINITE-ELEMENTE-METHODE (NUMERISCHE MATHEMATIK)
MEHRGITTERVERFAHREN + GITTERERZEUGUNG (NUMERISCHE MATHEMATIK)
Uncertainty quantification
Residual a-posteriori error estimation
ELLIPTISCHE DIFFERENTIALGLEICHUNGEN (ANALYSIS)
PARTIELLE DIFFERENTIALGLEICHUNGEN HÖHERER ORDNUNG (NUMERISCHE MATHEMATIK)
GALERKIN-VERFAHREN (NUMERISCHE MATHEMATIK)
FINITE ELEMENT METHOD (NUMERICAL MATHEMATICS)
Adaptive Finite Element Methods
ELLIPTIC DIFFERENTIAL EQUATIONS (MATHEMATICAL ANALYSIS)
FOS: Mathematics
Applied mathematics
Boundary value problem
ddc:510
Contraction (operator theory)
Mathematics
Numerical Analysis
65N30
Adaptive algorithm
Applied Mathematics
Estimator
Finite element method
Computational Mathematics
Asymptotically optimal algorithm
Modeling and Simulation
Norm (mathematics)
Analysis
Zdroj: Research Report, 2014-01 (01)
ISSN: 1290-3841
0764-583X
DOI: 10.1051/m2an/2015017
Popis: 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.
Research Report, 2014-01 (01)
Databáze: OpenAIRE
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