Finite element collocation methods for first-order systems

Abstract

Finite element methods and the associate collocation methods are considered for solving first-order hyperbolic systems, positive in the sense of Friedrichs. Applied in the case when the meshes are rectangle, those methods lead for example to the successfully used box scheme for the heat equation or D.S.N. scheme for the neutron transport equation. Generalizations of these methods are described here for nonrectangle meshes and (or) noncylindrical domains; stability results and error estimates are derived.