An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation

Dond, Asha K and Gudi, Thirupathi and Sau, Ramesh CH (2019) An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation. In: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 40 (4). pp. 421-460.

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Abstract

In this article, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints. A priori error estimates of optimal order are derived for velocity and pressure in the energy norm and the L-2-norm, respectively. Moreover, a reliable and efficient a posteriori error estimator is derived. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. In particular, we consider the abstract results with suitable stable pairs of velocity and pressure spaces like as the lowest-order Crouzeix-Raviart finite element and piecewise constant spaces, piecewise linear and constant finite element spaces. The theoretical results are illustrated by the numerical experiments.

Item Type:	Journal Article
Publication:	NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
Publisher:	TAYLOR & FRANCIS INC
Additional Information:	Copyright of this article belongs to TAYLOR & FRANCIS INC
Keywords:	Control-constraints; discontinuous Galerkin method; error bounds; finite element method; PDE-constrained optimization; Stokes equation
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 May 2019 07:11
Last Modified:	29 May 2019 09:31
URI:	http://eprints.iisc.ac.in/id/eprint/62471

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