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This paper focusses on the optimal control problems governed by fourth-orderlinear elliptic equations with clamped boundary conditions in the framework ofthe Hessian discretisation method (HDM). The HDM is an abstract framework thatenables the convergence analysis of numerical methods through a quadrupletknown as a Hessian discretisation (HD) and three core properties of HD. The HDMcovers several numerical schemes such as the conforming finite element methods,the Adini and Morley non-conforming finite element methods (ncFEMs), methodbased on gradient recovery (GR) operators and the finite volume methods (FVMs).Basic error estimates and superconvergence results are established for thestate, adjoint and control variables in the HDM framework. The articleconcludes with numerical results that illustrates the theoretical convergencerates for the GR method, Adini ncFEM and FVM.

Numerical analysis of optimal control problems governed by fourth-order linear elliptic equations using the Hessian discretisation method