Uniformly convergent adaptive methods for a class of parametric operator equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, p. 1485-1508

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.

DOI : https://doi.org/10.1051/m2an/2012013
Classification:  35R60,  47B80,  65C20,  65N12,  65N22,  65J10
Keywords: parametric partial differential equations, partial differential equations with random coefficients, uniform convergence, adaptive methods, operator equations
@article{M2AN_2012__46_6_1485_0,
     author = {Gittelson, Claude Jeffrey},
     title = {Uniformly convergent adaptive methods for a class of parametric operator equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {6},
     year = {2012},
     pages = {1485-1508},
     doi = {10.1051/m2an/2012013},
     zbl = {1276.65068},
     mrnumber = {2996337},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2012__46_6_1485_0}
}
Gittelson, Claude Jeffrey. Uniformly convergent adaptive methods for a class of parametric operator equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, pp. 1485-1508. doi : 10.1051/m2an/2012013. http://www.numdam.org/item/M2AN_2012__46_6_1485_0/

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