Displaying similar documents to “A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy”

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise, Sarah Cochez-Dhondt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into . We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete...

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...

Postprocessing of a finite volume element method for semilinear parabolic problems

Min Yang, Chunjia Bi, Jiangguo Liu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study a postprocessing procedure for improving accuracy of the finite volume element approximations of semilinear parabolic problems. The procedure amounts to solve a source problem on a coarser grid and then solve a linear elliptic problem on a finer grid after the time evolution is finished. We derive error estimates in the and norms for the standard finite volume element scheme and an improved error estimate in the ...