A SUPERCONVERGENT L∞-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT | Zendy

Yuelong Tang | Zendy; Yuchun Hua | Zendy

Open Access

A SUPERCONVERGENT <i>L</i><sup>∞</sup>-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT

Author(s) -

Yuelong Tang,

Yuchun Hua

Publication year - 2017

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 - 10.11948/2017065

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

In this paper, we investigate the superconvergence property of mixed finite element methods for a linear elliptic control problem with an integral constraint. The state and co-state are approximated by the order k = 1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. A superconvergent approximation of the control variable u will be constructed by a projection of the discrete adjoint state. It is proved that this approximation have convergence order h in L∞-norm. Finally, a numerical example is given to demonstrate the theoretical results.

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