Uniformly convergent adaptive methods for a class of parametric operator equations∗

Claude Jeffrey Gittelson

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1485-1508
  • ISSN: 0764-583X

Abstract

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We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.

How to cite

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Gittelson, Claude Jeffrey. "Uniformly convergent adaptive methods for a class of parametric operator equations∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1485-1508. <http://eudml.org/doc/276377>.

@article{Gittelson2012,
abstract = {We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.},
author = {Gittelson, Claude Jeffrey},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Parametric partial differential equations; partial differential equations with random coefficients; uniform convergence; adaptive methods; operator equations; parametric partial differential equations},
language = {eng},
month = {6},
number = {6},
pages = {1485-1508},
publisher = {EDP Sciences},
title = {Uniformly convergent adaptive methods for a class of parametric operator equations∗},
url = {http://eudml.org/doc/276377},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Gittelson, Claude Jeffrey
TI - Uniformly convergent adaptive methods for a class of parametric operator equations∗
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/6//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1485
EP - 1508
AB - We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
LA - eng
KW - Parametric partial differential equations; partial differential equations with random coefficients; uniform convergence; adaptive methods; operator equations; parametric partial differential equations
UR - http://eudml.org/doc/276377
ER -

References

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