Zienkiewicz, O. C.; Taylor, R. L. Finite element method. Vol. 3: Fluid dynamics. 5th ed. (English) Zbl 0991.74004 Oxford: Butterworth-Heinemann. 352 p. (2000). This volume appears for the first time as a separate book in the fundamental treatment by Zienkiewicz and Taylor of problems of fluid mechanics using FEM. It is entirely independent of the previous two volumes [see the foregoing entries]. The book considers the mechanics of compressible and incompressible fluids and gases, turbulence, buoyancy driven flows, and traditional problems of shallow water waves. The main point, as in the whole book, is the implementation of workable algorithms based on FEM, and the evaluation of their accuracy and applicability. The main solution method is a characteristic-based split algorithm proposed by the authors. All steps of problem solutions, as well as the final results obtained, are explained with brilliant clarity. This volume is recommended to practical engineers in fluid dynamics as well as to researchers in the area. Mathematicians can find a large number of open problems on the convergence of FEM for many practical situations. Reviewer: L.P.Lebedev (Rostov-na-Donu) Cited in 2 ReviewsCited in 51 Documents MSC: 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics 76M10 Finite element methods applied to problems in fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:finite element method; characteristic-based split algorithm; incompressible fluid; compressible fluid; buoyancy driven flows; turbulence; discretization; error estimate; Navier-Stokes equations; shallow water waves Citations:Zbl 0991.74005; Zbl 0991.74006 PDFBibTeX XMLCite \textit{O. C. Zienkiewicz} and \textit{R. L. Taylor}, Finite element method. Vol. 3: Fluid dynamics. 5th ed. Oxford: Butterworth-Heinemann (2000; Zbl 0991.74004)