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Sharp upper global a posteriori error estimates for nonlinear elliptic variational problems

János Karátson, Sergey Korotov (2009)

Applications of Mathematics

The paper is devoted to the problem of verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model embracing nonlinear elliptic variational problems is considered in this work. Based on functional type estimates developed...

Solution for a classical problem in the calculus of variations via rationalized Haar functions

Mohsen Razzaghi, Yadollah Ordokhani (2001)

Kybernetika

A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.

Stick-slip transition capturing by using an adaptive finite element method

Nicolas Roquet, Pierre Saramito (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical modeling of the fully developed Poiseuille flow of a newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...

Stick-slip transition capturing by using an adaptive finite element method

Nicolas Roquet, Pierre Saramito (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...

Structural Properties of Solutions to Total Variation Regularization Problems

Wolfgang Ring (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.

Superconvergence analysis and a posteriori error estimation of a Finite Element Method for an optimal control problem governed by integral equations

Ningning Yan (2009)

Applications of Mathematics

In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type a posteriori error estimator is provided, which can be used for adaptive mesh refinement.

The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch, Stefan Volkwein (2001)

ESAIM: Control, Optimisation and Calculus of Variations

A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...

The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch, Stefan Volkwein (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...

Un algoritmo de programación geométrica basado en funciones penalidad-multiplicadoras.

Eduardo Ramos Méndez (1986)

Trabajos de Investigación Operativa

El trabajo presenta un nuevo algoritmo para la resolución de un problema de porgramación geométrica primal transformado. El método se basa en las técnicas de tipo lagrangiano aumentado y utiliza como penalidad funciones derivadas de la exponencial para las restricciones con un único término, y de la pérdida cuadrática para las restricciones con más de un término. El problema resultante se resuelve por medio de un método lagrangiano con iteración de tipo Newton, y los parámetros de penalización se...

Currently displaying 81 – 100 of 105