A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints

• Published in: Computational optimization and applications Vol. 47; no. 1; pp. 133 - 159
• Main Author: Wollner, W.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.09.2010; Springer Nature B.V
• Subjects: Convex and Discrete Geometry; Discretization; Error analysis; Errors; Estimates; Finite element analysis; Finite element method; Management Science; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Methods; Operations Research; Operations Research/Decision Theory; Optimization; Partial differential equations; Statistics; Studies; Finite element method; Gradient constraints; Optimal control; State constraints; A posteriori error estimates; Interior point methods; Mesh adaptivity
• ISSN: 0926-6003; 1573-2894
• DOI: 10.1007/s10589-008-9209-2

In this paper we are concerned with a posteriori error estimates for the solution of some state constraint optimization problem subject to an elliptic PDE. The solution is obtained using an interior point method combined with a finite element method for the discretization of the problem. We will derive separate estimates for the error in the cost functional introduced by the interior point parameter and by the discretization of the problem. Finally we show numerical examples to illustrate the findings for pointwise state constraints and pointwise constraints on the gradient of the state.