Error Bounds for Discontinuous Finite Volume Discretisations of Brinkman Optimal Control Problems
J. Sci. Comput.(2018)
摘要
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.
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关键词
A priori error analysis,Brinkman equations,Discontinuous finite volume methods,Optimal control problem,Variational control discretisation
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