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Full Description
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.
Contents
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
