Boundary concentrated finite elements for optimal control problems with distributed observation

S. Beuchler (), K. Hofer (), D. Wachsmuth () and J.-E. Wurst ()

Computational Optimization and Applications, 2015, vol. 62, issue 1, 65 pages

Abstract: We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a $$H^{1+\delta }(\Omega )$$ H 1 + δ ( Ω ) regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the $$L_2$$ L 2 norm decreases like $$N^{-\delta }$$ N - δ , where $$N$$ N is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of $$\Omega $$ Ω . We present several numerical results. Copyright Springer Science+Business Media New York 2015

Keywords: Optimal control; Elliptic partial differential equation; Higher-order discretization; Boundary-concentrated finite elements; A priori error estimates (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-015-9737-5

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