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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.)