Abstract
In this paper, we discuss the convergence analysis of discontinuous finite volume methods applied to distribute the optimal control problems governed by a class of second-order linear elliptic equations. In order to approximate the control, two different methodologies are adopted: one is the method of variational discretization and second is piecewise constant discretization technique. For variational discretization method, optimal order of convergence in the [Formula: see text]-norm for state, adjoint state and control variables is derived. Moreover, optimal order of convergence in discrete [Formula: see text]-norm is also derived for state and adjoint state variables. Whereas, for piecewise constant approximation of control, first order convergence is derived for control, state and adjoint state variables in the [Formula: see text]-norm. In addition to that, optimal order of convergence in discrete [Formula: see text]-norm is derived for state and adjoint state variables. Also, some numerical experiments are conducted to support the derived theoretical convergence rate.
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