Estimates of the Distance to the Set of Solenoidal Vector Fields and Applications to A Posteriori Error Control

Repin, Sergey
October 2015
Computational Methods in Applied Mathematics;Oct2015, Vol. 15 Issue 4, p515
Academic Journal
No abstract available.


Related Articles

  • A posteriori error estimates for the generalized Stokes problem. Repin, S.; Stenberg, R. // Journal of Mathematical Sciences;Apr2007, Vol. 142 Issue 1, p1828 

    The paper concerns a posteriori estimates of functional type for the difference between exact and approximate solutions to a generalized Stokes problem. The estimates are derived by transformations of the basic integral identity defining a generalized solution to the problem using the method...

  • Constants within Error Estimates for Legendre-Galerkin Spectral Approximations of Control-Constrained Optimal Control Problems. Jianwei Zhou // Abstract & Applied Analysis;2014, p1 

    Explicit formulae of constants within the a posteriori error estimate for optimal control problems are investigated with Legendre-Galerkin spectral methods. The constrained set is put on the control variable. For simpleness, one-dimensional bounded domain is taken. Meanwhile, the corresponding a...

  • A posteriori error estimates for optimal control problems constrained by convection-diffusion equations. Fu, Hongfei; Rui, Hongxing; Zhou, Zhaojie // Frontiers of Mathematics in China;Feb2016, Vol. 11 Issue 1, p55 

    We propose a characteristic finite element discretization of evolutionary type convection-diffusion optimal control problems. Nondivergence-free velocity fields and bilateral inequality control constraints are handled. Then some residual type a posteriori error estimates are analyzed for the...

  • A Review of Unified A Posteriori Finite Element Error Control. Carstensen, C.; Eigei, M.; Hoppe, R. H. W.; Löbhard, C. // Numerical Mathematics: Theory, Methods & Applications;Nov2012, Vol. 5 Issue 4, p509 

    This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential equations. In the abstract setting of mixed formulations, a generalised formulation of the corre-sponding residuals is proposed which then...

  • A POSTERIORI ERROR ESTIMATES OF hp-FEM FOR OPTIMAL CONTROL PROBLEMS. Wei Gong; Liu, Wenbin; Ningning Yan // International Journal of Numerical Analysis & Modeling;2011, Vol. 8 Issue 1, p48 

    In this paper, we investigate a posteriori error estimates of the hp-finite element method for a distributed convex optimal control problem governed by the elliptic partial differential equations. A family of weighted a posteriori error estimators of residual type are formulated. Both...

  • A posteriori error estimates for the fractional optimal control problems. Ye, Xingyang; Xu, Chuanju // Journal of Inequalities & Applications;9/9/2015, Vol. 2015 Issue 1, p1 

    In this paper, we study the spectral approximation for a constrained optimal control problem governed by the time fractional diffusion equation. A posteriori error estimates are obtained for both the state and the control approximations. Some numerical experiments are carried out to show that...

  • A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE. Danping Yang; Yanzhen Chang; Wenbin Liu // Journal of Computational Mathematics;Jul2008, Vol. 26 Issue 4, p471 

    In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by...

  • Residual Based A Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations. Ming Cui; Ningning Yan // Numerical Mathematics: Theory, Methods & Applications;Nov2012, Vol. 5 Issue 4, p602 

    In this paper, we derive a posteriori error estimates for finite element ap-proximations of the optimal control problems governed by the Stokes-Darcy system. We obtain a posteriori error estimators for both the state and the control based on the resid-ual of the finite element approximation. It...

  • LOCAL A PRIORI AND A POSTERIORI ERROR ESTIMATE OF TQC9 ELEMENT FOR THE BIHARMONIC EQUATION. Ming Wang; Weimeng Zhang // Journal of Computational Mathematics;Mar2008, Vol. 26 Issue 2, p196 

    In this paper, local a priori, local a posteriori and global a posteriori error estimates are obtained for TQC9 element for the biharmonic equation. An adaptive algorithm is given based on the a posteriori error estimates.

  • On computational methods for variational inequalities. Suttmeier, F. T. // Computational Mechanics;Jun2005, Vol. 35 Issue 6, p401 

    In this note, we focus on optimised mesh design for the Finite Element (FE) method for variational inequalities using global norm estimates for local error control. The strategies are based on the so called dual-weighted-residual (DWR) approach to a posteriori error control for FE-schemes (see,...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics