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Incompressible flow and the finite element method. Vol. 1: Advection-diffusion. Vol. 2: Isothermal laminar flow. (English) Zbl 0988.76005
Chichester: Wley; 0-471-49249-3 (vol. 1); 0-471-49250-7 (vol. 2)). 1112 p., £45.00; EUR 74.30/pbk (per vol.) (2000).
Publisher’s description (no review copy received): This comprehensive reference work covers all important details regarding the application of the finite element method to incompressible flows. It addresses the theoretical background and the detailed development of appropriate numerical methods applied to the solution of a wide range of incompressible flows, beginning with extensive coverage of the advection-diffusion equation in volume one. For both this equation and the equations of principal interest – the Navier-Stokes equations, covered in detail in volume two – detailed discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained.
Together, this two-volume work explains and emphasizes consistency in six areas: consistent mass matrix; consistent pressure Poisson equation; consistent penalty methods; consistent normal direction; consistent heat flux; consistent forces. Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76Rxx Diffusion and convection
76D05 Navier-Stokes equations for incompressible viscous fluids