Generalized Petrov–Galerkin methods for the numerical solution of Burgers' equation

Abstract

Abstract Generalized Petrov–Galerkin methods are applied in two different ways for the numerical solution of Burgers' equation. In the first place, it is used to produce upwinding in the way described by Mitchell and Griffiths. 9,10 The main objective of this paper is in the second place to use it as a moving finite element method. In particular, it is shown that the methods of Miller and co‐workers 4–6 and Herbst et al. 7,8 can be incorporated in the more general approach presented in this paper. Several choices for the test functions are discussed and numerical results are given.