Convergence and Quasi-Optimality of an Adaptive FEM via INF-SUP Stability for a Dirichlet Boundary Control Problem
Abstract
Abstract. In this article, an energy-space based approach is proposed for the Dirichlet boundary control problem, and the constraint is given by a general second-order linear PDE. Then a finite element based numerical method is designed and analyzed for its numerical approximation. Both a priori and a posteriori error estimates in the energy norm are derived. Quasi-orthogonality is shown using the result of M. Feischl [ Math. Comp., 91 (2022), pp. 2059–2094]. Finally, the convergence and quasi-optimal rate of convergence of an adaptive finite element method are shown for the proposed Dirichlet boundary control problem. The theoretical results are illustrated by the numerical experiments.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Stability and Controllability of Differential Equations
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 1
- Pages
- 288–315
- Publication date
- 13 January 2026
- Language
- EN