Dynamical systems flow computation by adaptive triangulation methods (Q1960891)

This paper is concerned with the numerical computation of the evolution of two-dimensional compact manifolds under the flow of dynamical systems. In the first part of the paper, after introducing the theoretical framework, the author presents the classical approach, called the domain method, which is based in triangulation algorithms similar to those used in finite element methods in partial differential equations. Then a second approach, called image methods, in which the adaptive triangulation operates directly on the flow is presented. Finally the results of some numerical experiments concerning the three-dimensional Lorentz equations are presented. The author compares the above two methods for a compact two-dimensional manifold chosen arbitrarily and concludes that although domain methods are reliable for many applications adaptive image methods show a better performance due to its flexibility in the triangulation process.