Work

A posteriori error analysis for optimization with PDE constraints

Year: 2025

Type: article

Abstract: We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a posteriori bounds capturing the approximation of the state, the adjoint state, the control and the observation. The upper and lower bounds show a gap, which grows with decreasing cost or Tikhonov regularization parameter. This growth is mitigated compared to previous results and can be countered by refinement if control and observation involve compact operators. Numerical results illustrate these properties for model problems with distributed and boundary control.

Source: Mathematical Control and Related Fields

DOI: 10.3934/mcrf.2025042

Authors: Fernando Gaspoz, Christian Kreuzer, Andreas Veeser, Winnifried Wollner

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional del Litoral, TU Dortmund University, University of Milan, Universität Hamburg

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional del Litoral, Agencia Nacional de Promoción Científica y Tecnológica

Awards: G3324083048, G4777107596, G7589763286, G955525907