A GLOBAL SUPERCONVERGENT L∞-ERROR ESTIMATE OF MIXED FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS | Zendy

Li Li | Zendy

Open Access

A GLOBAL SUPERCONVERGENT <i>L</i><sup>∞</sup>-ERROR ESTIMATE OF MIXED FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS

Author(s) -

Li Li

Publication year - 2015

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2015028

Subject(s) - superconvergence , mathematics , piecewise , finite element method , norm (philosophy) , optimal control , projection (relational algebra) , mathematical analysis , physics , mathematical optimization , algorithm , political science , law , thermodynamics

In this paper, we discuss the superconvergence of mixed finite element methods for a semilinear elliptic control problem with an integral constraint. The state and costate are approximated by the order $k=1$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Approximation of the optimal control of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state. It is proved that this approximation has convergence order $h^{2}$ in $L^{\infty}$-norm. Finally, a numerical example is given to demonstrate the theoretical results.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research