Work

Numerical analysis of a nonsmooth quasilinear elliptic control problem

Year: 2025

Type: article

Abstract: In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state variable. Despite the lack of differentiability of the non-linearity in the quasilinear elliptic equation, the corresponding control-to-state operator is of class C 1 but not of class C 2 . Analogously, the discrete control-to-state operators associated with the approximated control problems are proven to be of class C 1 only. By using an explicit second-order sufficient optimality condition, we prove a priori error estimates for a variational approximation, a piecewise constant approximation, and a continuous piecewise linear approximation of the continuous optimal control problem. The numerical tests confirm these error estimates.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025086

Authors: Christian Clason, Huu Nhu Vu, Arnd Rösch

Institutions: University of Graz, Nawi Graz, University of Duisburg-Essen, Phenikaa University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: Deutsche Forschungsgemeinschaft