Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs
Open access
Date
2011-05Type
- Report
ETH Bibliography
yes
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Abstract
We investigate existence and regularity of a class of semilinear, parametric elliptic PDEs with affine dependence of the principal part of the differential operator on countably many parameters. We establish a-priori estimates and analyticity of the parametric solutions. We establish summability results of coefficient sequences of polynomial chaos type expansions of the parametric solutions in terms of tensorized Taylor-, Legendre- and Chebyshev polynomials on the infinite-dimensional parameter domain. We deduce rates of convergence for N term truncated approximations of expansions of the parametric solution. We also deduce spatial regularity of the solution, and establish convergence rates of N -term discretizations of the parametric solutions with respect to these polynomials in parameter space and with respect to a multilevel hierarchy of Finite Element spaces in the spatial domain of the PDE. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010403202Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Semilinear elliptic partial differential equations; Infinite dimensional spaces; N-term approximation; Analyticity in Infinite Dimensional Spaces; Tensor Product Taylor-; Legendre- and Chebyshev polynomial ApproximationOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Funding
247277 - Automated Urban Parking and Driving (EC)
Related publications and datasets
Is previous version of: http://hdl.handle.net/20.500.11850/67336
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ETH Bibliography
yes
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