Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations

With numerous applications, particularly in fluid dynamics, the semi-Lagrangian approximation scheme is an essential part of the numerical analyst’s toolkit. This largely self-contained book provides a framework for the semi-Lagrangian strategy for 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 cover high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The text brings together developments from a wide range of sources to provide a unified treatment of the subject. This book is written for graduate and advanced undergraduate courses on numerical methods, and for researchers and practitioners whose work involves numerical analysis of hyperbolic PDEs.