Displaying similar documents to “Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints”

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...

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

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We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k + 1 in the L 2 -norm if the method uses polynomials of order k . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k + 1 . Further we consider a residual-based...

Finite element analysis for unilateral problems with obstacles on the boundary

Jaroslav Haslinger (1977)

Aplikace matematiky

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Finite element analysis of unilateral problems with obstacles on the boundary is given. Provided the exact solution is smooth enough, we obtain the rate of convergence 0 ( h ) for the case of one and two (lower and upper) obstacles on the boundary. At the end of this paper the proof of convergence without any regularity assumptions on the exact solution u is given.

A posteriori error estimates for the 3 D stabilized Mortar finite element method applied to the Laplace equation

Zakaria Belhachmi (2003)

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

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We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also...

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 ...