Displaying similar documents to “An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints”

estimates for the Cahn–Hilliard equation with obstacle free energy

Ľubomír Baňas, Robert Nürnberg (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm.

Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2004)

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

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We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the...

Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

Eduardo Casas (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L ∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint...

Residual  error estimators for contact problems in elasticity

Patrick Hild, Serge Nicaise (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with the unilateral contact problem in linear elasticity. We define two error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.