A Priori Mesh Grading for Distributed Optimal Control Problems

This paper deals with L2-error estimates for finite element approximations of control constrained distributed optimal control problems governed by linear partial differential equations. First, general assumptions are stated that allow to prove second-order convergence in control, state and adjoint state. Afterwards these assumptions are verified for problems where the solution of the state equation has singularities due to corners or edges in the domain or nonsmooth coefficients in the equation. In order to avoid a reduced convergence order, graded finite element meshes are used.

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