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Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations. (English) Zbl 1335.65001
Other Titles in Applied Mathematics 133. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-304-4; 978-1-61197-305-1/ebook). xii, 319 p. (2014).
Publisher’s description: This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.

MSC:
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65K10 Numerical optimization and variational techniques
35F21 Hamilton-Jacobi equations
49J20 Existence theories for optimal control problems involving partial differential equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49M25 Discrete approximations in optimal control
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