Recovery type superconvergence and a posteriori error estimates for control problems governed by Stokes equations

Authors:
Huipo Liu;Ningning Yan
Affiliations:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, we derive recovery type superconvergence analysis and a posteriori error estimates for the finite element approximation of the distributed optimal control governed by Stokes equations. We obtain superconvergence results and asymptotically exact a posteriori error estimates by applying two recovery methods, which are the patch recovery technique and the least-squares surface fitting method. Our results are based on some regularity assumption for the Stokes control problems and are applicable to the first order conforming finite element method with regular but nonuniform partitions.