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

Priv.-Doz. Dr. Sven Beuchler

May 18, 2010, 3:30 p.m. HF 136

We investigate the discretization of optimal boundary control problems for elliptic equations by the boundary concentrated finite element method. We prove that the discretization error $\left\Vert u^∗ − u_h^∗ \right\Vert_{L^2(Γ)}$ 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 $N^{−3/4}$ . Moreover, we present an algorithm that solves the discretized problem in almost optimal complexity. The talk is complemented with numerical results.

This is a joint work with D. Wachsmuth (RICAM) and C. Pechstein (Numa, JKU Linz).