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Adaptive modeling for free-surface flows

Simona Perotto (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable “combination” of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex model (with...

Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems

Rudolf L. Voller (1992)

Applications of Mathematics

In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.

An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators

A. Renaud, G. Cohen (2010)

ESAIM: Control, Optimisation and Calculus of Variations

To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial Dunn properties...

An improved convergence analysis of Newton's method for twice Fréchet differentiable operators

Ioannis K. Argyros, Sanjay K. Khattri (2013)

Applicationes Mathematicae

We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.

An Iterative Procedure for Solving Nonsmooth Generalized Equation

Marinov, Rumen Tsanev (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47H04, 65K10.In this article, we study a general iterative procedure of the following form 0 ∈ f(xk)+F(xk+1), where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations in the nonsmooth framework. We prove that this method is locally Q-linearly convergent to x* a solution of the generalized equation 0 ∈ f(x)+F(x) if the set-valued map [f(x*)+g(·)−g(x*)+F(·)]−1 is Aubin continuous...

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