Geometric Partial Differential Equations - Part 2: Volume 22

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.

Autorentext
Andrea Bonito is professor in the Department of Mathematics at Texas A&M University.

Together with Ricardo H. Nochetto they have more than forty years of experience in the variational formulation and approximation of a wide range of geometric partial differential equations (PDEs). Their work encompass fundamental studies of numerical PDEs: the design, analysis and implementation of efficient numerical algorithms for the approximation of PDEs; and their applications in modern engineering, science, and bio-medical problems. Ricardo H. Nochetto is professor in the Department of Mathematics and the Institute for Physical Science and Technology at the University of Maryland, College Park.

Together with Andrea Bonito they have more than forty years of experience in the variational formulation and approximation of a wide range of geometric partial differential equations (PDEs). Their work encompass fundamental studies of numerical PDEs: the design, analysis and implementation of efficient numerical algorithms for the approximation of PDEs; and their applications in modern engineering, science, and bio-medical problems.

Inhalt

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