Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs (Q429474)

The authors investigate the discretization of optimal boundary control problems for elliptic equations on two-dimensional polygonal domains by the boundary concentrated finite element method. They prove that the discretization error decreases like \(N^{-1}\), where \(N\) is the total number of unknowns. This makes the proposed method favorable in comparison to the h-version of the finite element method, where the discretization error behaves like \(N^{-3/4}\) for uniform meshes. Moreover, they present an algorithm that solves the discretized problem in almost optimal complexity. The paper is complemented with numerical results.