Error Bounds for Discontinuous Finite Volume Discretisations of Brinkman Optimal Control Problems

S. Kumar, R. Ruiz-Baier, R. Sandilya

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2 Citations (Scopus)

Abstract

We introduce a discontinuous finite volume method for the approximation of distributed optimal control problems governed by the Brinkman equations, where a force field is sought such that it produces a desired velocity profile. The discretisation of state and co-state variables follows a lowest-order scheme, whereas three different approaches are used for the control representation: a variational discretisation, and approximation through piecewise constant and piecewise linear elements. We employ the optimise-then-discretise approach, resulting in a non-symmetric discrete formulation. A priori error estimates for velocity, pressure, and control in natural norms are derived, and a set of numerical examples is presented to illustrate the performance of the method and to confirm the predicted accuracy of the generated approximations under various scenarios.

Original languageEnglish
Pages (from-to)64-93
Number of pages30
JournalJournal of Scientific Computing
Volume78
Issue number1
DOIs
Publication statusPublished - 15 Jan 2019
Externally publishedYes

Keywords

  • A priori error analysis
  • Brinkman equations
  • Discontinuous finite volume methods
  • Optimal control problem
  • Variational control discretisation

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