PDE-constrained optimization within FreeFEM

By: Frédéric Hecht, Gontran Lance, Emmanuel Trélat

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eText | 6 May 2026

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PDE constrained optimization problems are frequently encountered in many academic or industrial contexts. This book shows how to attack and solve a given PDE constrained optimization problem thanks to the efficient and expert tool FreeFEM.

This book is intended for students and researchers aiming at learning how to efficiently solve, with the software FreeFEM, optimization problems under partial differential equations (PDE) constraints. The readers are expected to have a basic knowledge in the analysis and numerical solving of partial differential equations with finite element methods, in optimization, in algorithmics and numerical implementation.

All the codes are available at FreeFEM's github and can hopefully serve as templates for the users.