Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions | Zendy

Niklas Behringer | Zendy

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Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions

Author(s) -

Niklas Behringer

Publication year - 2020

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2020038

Subject(s) - pointwise , optimal control , convergence (economics) , mathematics , tracking error , approximation error , point (geometry) , tracking (education) , mathematical optimization , control (management) , mathematical analysis , computer science , geometry , psychology , pedagogy , artificial intelligence , economics , economic growth

This work is motivated by recent interest in the topic of pointwise tracking type optimal control problems for the Stokes problem. Pointwise tracking consists of point evaluations in the objective functional which lead to Dirac measures appearing as source terms of the adjoint problem. Considering bounds for the control allows for improved regularity results for the exact solution and improved approximation error estimates of its numerical counterpart. We show a sub-optimal convergence result in three dimensions that nonetheless improves the results known from the literature. Finally, we offer supporting numerical experiments and insights towards optimal approximation error estimates.

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