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1st Edition - January 26, 2021
Editors: Andrea Bonito, Ricardo Horacio Nochetto
Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They… Read more
Immediately download your ebook while waiting for your print delivery. No promo code is needed.
Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering.
The targeted audience is mathematically trained research scientists and engineers with basic knowledge in partial differential equations and their numerical approximations.
1. Shape and topology optimization
Grégoire Allaire, Charles Dapogny, and François Jouve
2. Optimal transport: discretization and algorithms
Quentin Mérigot and Boris Thibert
3. Optimal control of geometric partial differential equations
Michael Hintermüller and Tobias Keil
4. Lagrangian schemes for Wasserstein gradient flows
Jose A. Carrillo, Daniel Matthes, and Marie-Therese Wolfram
5. The Q-tensor model with uniaxial constraint
Juan Pablo Borthagaray and Shawn W. Walker
6. Approximating the total variation with finite differences or finite elements
Antonin Chambolle and Thomas Pock
7. Numerical simulation and benchmarking of drops and bubbles
Stefan Turek and Otto Mierka
8. Smooth multi-patch discretizations in isogeometric analysis
Thomas J.R. Hughes, Giancarlo Sangalli, Thomas Takacs, and Deepesh Toshniwal
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