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This comprehensive two volume reference work is devoted to the
important details regarding the application of the finite element
method to incompressible flows, addressing the theoretical
background and the detailed development of appropriate numerical
methods applied to their solution. Volume One provides extensive
coverage of the prototypical fluid mechanics equation: the
advection-diffusion equation. In addition, for both this equation
and the equations of principal interest - the Navier-Stokes
equations - (covered in detail in Volume Two), a discussion of both
the continuous and discrete equations is presented. Also addressed
are explanations of how to properly march the time-dependent
equations using smart implicit methods. Boundary and initial
conditions, so important in applications, are thoroughly 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:
This comprehensive two-volume reference covers the application of
the finite element method to incompressible flows in fluid
mechanics, addressing the theoretical background and the
development of appropriate numerical methods applied to their
solution.
This comprehensive reference work covers all the 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.
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