TITLE

WEAK-DUALITY BASED ADAPTIVE FINITE ELEMENT METHODS FOR PDE-CONSTRAINED OPTIMIZATION WITH POINTWISE GRADIENT STATE-CONSTRAINTS

AUTHOR(S)
Hintermiiller, M.; Hinze, Michael; Hoppe, Ronald H.W.
PUB. DATE
March 2012
SOURCE
Journal of Computational Mathematics;Mar2012, Vol. 30 Issue 2, p101
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Adaptive finite element methods for optimization problems for second order linear el-liptic partial differential equations subject to pointwise constraints on the £2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteri¬ori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.
ACCESSION #
83446984

 

Related Articles

  • Pointwise error estimate and asymptotic error expansion inequalities for a stabilized Galerkin method. JAEUN KU // IMA Journal of Numerical Analysis;Jan2011, Vol. 31 Issue 1, p165 

    This paper contains new pointwise error estimates for a stabilized Galerkin method proposed by Bramble et al. (1998, Comput. Methods Appl. Mech. Eng., 152, 195–210) and Ku (2007, Math. Comput., 76, 97–114) for second-order elliptic partial differential equations. The estimates show...

  • A Posteriori Error Analysis for Anisotropic Elliptic Problem. Achchab, B.; Majdoubi, A.; Souissi, A. // AIP Conference Proceedings;9/30/2010, Vol. 1281 Issue 1, p1555 

    In this work, we propose a robust a posteriori error estimator for approximations solution of anisotropic elliptic partial differential equations with the nonconforming finite elements method, we adopt the error in constitutive law approach.

  • Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment. Hinze, Michael; Schiela, Anton // Computational Optimization & Applications;Apr2011, Vol. 48 Issue 3, p581 

    n adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems...

  • 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...

  • TWO-SCALE FINITE ELEMENT DISCRETIZATIONS FOR PARTIAL DIFFERENTIAL EQUATIONS. Fang Liu; Aihui Zhou // Journal of Computational Mathematics;May2006, Vol. 24 Issue 3, p373 

    Some two-scale finite element discretizations are introduced for a class of linear partial differential equations. Both boundary value and eigenvalue problems are studied. Based on tile two-scale error resolution techniques, several two-scale finite element algorithms are proposed and analyzed....

  • A Coupling Method of New EMFE and FE for Fourth-Order Partial Differential Equation of Parabolic Type. Yang Liu; Hong Li; Zhichao Fang; Siriguleng He; Jinfeng Wang // Advances in Mathematical Physics;2013, p1 

    We propose and analyze a new numerical method, called a coupling method based on a new expanded mixed finite element (EMFE) and finite element (FE), for fourth-order partial differential equation of parabolic type. We first reduce the fourth-order parabolic equation to a coupled system of...

  • ERROR ESTIMATES FOR THE FINITE ELEMENT DISCRETIZATION OF SEMI-INFINITE ELLIPTIC OPTIMAL CONTROL PROBLEMS. Merinoy, Pedro; Neitzely, Ira; Tröltzschy, Fredi // Discussiones Mathematicae: Differential Inclusions, Control & Op;2010, Vol. 30 Issue 2, p221 

    In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate...

  • Vibrations of an Elastic Beam Induced by a Two Degrees of Freedom Oscillator. Pasheva, V. V.; Chankov, E. S.; Venkov, G. I.; Stoychev, G. B. // AIP Conference Proceedings;11/17/2009, Vol. 1184 Issue 1, p72 

    The dynamic response of an elastic beam attached to a spring rigid bar of two degrees of freedom is studied in this paper. The partial differential equation (PDE) describing the beam and the ordinary differential equations (ODEs) concerning the rigid bar are transformed into a homogeneous first...

  • A Fast Numerical Method for a Nonlinear Black-Scholes Equation. Koleva, Miglena N.; Vulkov, Lubin G. // AIP Conference Proceedings;11/17/2009, Vol. 1184 Issue 1, p64 

    In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

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

Try another library?
Sign out of this library

Other Topics