NDLI: Reduced basis methods with adaptive snapshot computations

Content Provider	Springer Nature Link
Author	Urban, Karsten Ali, Mazen Steih, Kristina
Copyright Year	2016
Abstract	We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the standard RB ‘truth space’, but allow for error estimation of the RB approximation with respect to the exact solution of the considered parameterized partial differential equation. The residual-based a posteriori error estimators are computed by an adaptive dual wavelet expansion, which allows us to compute a surrogate of the dual norm of the residual. The resulting adaptive RBM is analyzed. We show the convergence of the resulting adaptive greedy method. Numerical experiments for stationary and instationary problems underline the potential of this approach.
Ending Page	294
Page Count	38
Starting Page	257
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	2
Volume Number	43
Language	English
Publisher	Springer US
Publisher Date	2016-10-22
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Adaptivity Visualization Computational Mathematics and Numerical Analysis Complexity and performance of numerical algorithms Mathematical and Computational Biology Approximation by other special function classes Computational Science and Engineering Multidimensional problems (should also be assigned at least one other classification number in this section) Wavelets Periodic solutions Mathematical Modeling and Industrial Mathematics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Reduced basis method
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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