Crouzeix-Raviart Finite Element Approximation of Dirichlet Boundary Control Problems with Piecewise Constant Controls

Sudipto Chowdhury; Shallu

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arXiv · 2604.17315

Crouzeix-Raviart Finite Element Approximation of Dirichlet Boundary Control Problems with Piecewise Constant Controls

Sudipto Chowdhury·Shallu

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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. Furthermore, it establishes an optimal order a priori error estimate for the control variable.

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BibTeX RIS

Sudipto Chowdhury, Shallu. 2026-04-19. Crouzeix-Raviart Finite Element Approximation of Dirichlet Boundary Control Problems with Piecewise Constant Controls. https://arxiv.org/abs/2604.17315

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