A posteriori error estimates for hp finite element solutions of convex optimal control problems

A posteriori error estimates for hp finite element solutions of convex optimal control problems

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Article ID: iaor20114460
Volume: 235
Issue: 12
Start Page Number: 3435
End Page Number: 3454
Publication Date: Apr 2011
Journal: Journal of Computational and Applied Mathematics
Authors: ,
Keywords: optimization, programming: convex
Abstract:

In this paper, we present a posteriori error analysis for h p equ1 finite element approximation of convex optimal control problems. We derive a new quasi‐interpolation operator of Clément type and a new quasi‐interpolation operator of Scott–Zhang type that preserves homogeneous boundary condition. The Scott–Zhang type quasi‐interpolation is suitable for an application in bounding the errors in L 2 equ2‐norm. Then h p equ3 a posteriori error estimators are obtained for the coupled state and control approximations. Such estimators can be used to construct reliable adaptive finite elements for the control problems.

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