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.
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
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.
