Displaying similar documents to “Estimating error bounds of Bajaj's solid models and their control hexahedral meshes.”

Two-sided a posteriori estimates of global and local errors for linear elliptic type boundary value problems

Hannukainen, Antti, Korotov, Sergey

Similarity:

The paper is devoted to the problem of reliable control of accuracy of approximate solutions obtained in computer simulations. This task is strongly related to the so-called 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. Mathematical model described by a linear elliptic (reaction-diffusion) equation with mixed boundary conditions...

An error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Hintermüller, Ronald H.W. Hoppe, Yuri Iliash, Michael Kieweg (2007)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We present an error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide...

Complementarity - the way towards guaranteed error estimates

Vejchodský, Tomáš

Similarity:

This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.

A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...

A comparison of some a posteriori error estimates for fourth order problems

Segeth, Karel

Similarity:

A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...