Year: 2024
Type: preprint
Abstract: This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It employs an ultra weak formulation and utilizes Crouzeix-Raviart finite elements to discretize the state variable, while employing piecewise constants for the control variable discretization. The study demonstrates that the energy norm of an enriched discrete optimal control is uniformly bounded with respect to the discretization parameter. Furthermore, it establishes an optimal order a priori error estimate for the control variable.
Source: arXiv (Cornell University)
Authors: Chowdhury, Sudipto, Garg, Divay
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391767091