Existence and approximation of solutions to nonlinear operator equations

Summary We consider the approximation of solutions to a nonlinear operator equation of the formLu+N(u)=f in a Hilbert space by the Rayleigh-Ritz-Galerkin method. Using a variant of Cesari's alternative method we determine when the existence of an approximation of orderk determines the existence of a solution to the equation and give a method to determine error bounds on the approximation.

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Zusammenfassung Wir benutzen das Rayleigh-Ritz-Galerkin'sche Verfahren um Lösungen der nichtlinearen Operatorgleichung vom TypLu+N (u)=f in einem Hilbertraum zu gewinnen. Eine Umformulierung der Cesari'schen alternativen Methode wird angewendet um die Frage zu lösen ob die Existenz einer Approximation der Ordnungk die Existenz einer exakten Lösung mit sich bringt. Eine Methode um Fehlerschranken für die Approximationen zu bestimmen wird angegeben.

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Supported in part by the DAAD/CONICYT, professor exchange program     

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Iterative methods for solving nonlinear irregular operator equations in banach space

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