Computational Galerkin methods.

*(English)*Zbl 0533.65069
Springer Series in Computational Physics. New York etc.: Springer-Verlag. XI, 309 p., 107 figs. DM 88.00; $ 32.90 (1984).

This book is, may be, the most interesting work on the Galerkin method. It starts with the ascertained fact that ”any problem for which governing equations can be written down is a candidate for a Galerkin method”. The work starts with the traditional variant of the Galerkin method, and finishes with generalizations of this method. In its course, the computational variant is treated, as well as the finite element variant, spectral methods, etc. Comparisons are also made between these methods and the finite differences method. It is remarkable that the author inquires and discusses about convergence, stability and accuracy. Relations with the boundary element method are made as well. The method is variously applied. But the most important applications are those in fluid dynamics. So, Burger’s equation is treated, problems linked to the behaviour of viscous and inviscid fluids, heat transfer, and boundary layer problems, all in the steady and unsteady variants. Regarding the finite element variant of the method the use of triangular and rectangular elements is discussed. The work ends with some Fortran subroutines for solving Burger’s equation. This all forms a beautiful pleading for the application of the Galerkin method in different fields of engineering.

Reviewer: T.Petrila

##### MSC:

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

35Q99 | Partial differential equations of mathematical physics and other areas of application |

35-04 | Software, source code, etc. for problems pertaining to partial differential equations |

76-04 | Software, source code, etc. for problems pertaining to fluid mechanics |

76Q05 | Hydro- and aero-acoustics |

76B99 | Incompressible inviscid fluids |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |