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

Li Li

doi:10.11948/2015028

2015 Volume 5 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2015 > 5(3): 313-328

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Li Li. A GLOBAL SUPERCONVERGENT L∞-ERROR ESTIMATE OF MIXED FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 313-328. doi: 10.11948/2015028

Citation:

Li Li. A GLOBAL SUPERCONVERGENT L^∞-ERROR ESTIMATE OF MIXED FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 313-328. doi: 10.11948/2015028

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

Li Li

Key Laboratory for Nonlinear Science and System Structure, School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, Chongqing, China

Abstract

Abstract

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 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. 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 h² in L^∞-norm. Finally, a numerical example is given to demonstrate the theoretical results.
- Semilinear elliptic equations /
- optimal control problems /
- superconvergence /
- mixed finite element methods /
- L^∞-error estimate
MSC: 49J20;65N30

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References

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