Geometric Pdes

Erscheinungsjahr 2020
ISBN: 978-0-444-64003-1
Verlag: NORTH HOLLAND

Buch, Englisch, Band 21, 710 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 1220 g

Reihe: Handbook of Numerical Analysis

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.

Zielgruppe

<p>The targeted audience is mathematically trained research scientists and engineers with basic knowledge in partial differential equations and their numerical approximations.</p>

Autoren/Hrsg.

Weitere Mitwirkende

Bonito, Andrea

Nochetto, Ricardo Horacio

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

1. Finite element methods for the Laplace-Beltrami operator Andrea Bonito, Alan Demlow and Ricardo H. Nochetto 2. The Monge-Ampère equation Michael Neilan, Abner J. Salgado and Wujun Zhang 3. Finite element simulation of nonlinear bending models for thin elastic rods and plates Sören Bartels 4. Parametric finite element approximations of curvature-driven interface evolutions John W. Barrett, Harald Garcke and Robert Nürnberg 5. The phase field method for geometric moving interfaces and their numerical approximations Qiang Du and Xiaobing Feng 6. A review of level set methods to model interfaces moving under complex physics: Recent challenges and advances Robert I. Saye and James A. Sethian 7. Free boundary problems in fluids and materials Eberhard Bänsch and Alfred Schmidt 8. Discrete Riemannian calculus on shell space Behrend Heeren, Martin Rumpf, Max Wardetzky and Benedikt Wirth

Über Autor(innen)

Bonito, Andrea
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.

Nochetto, Ricardo Horacio
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.