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Mathematical aspects of finite element methods for incompressible viscous flows. (English) Zbl 0668.76029
Finite elements. Theory and application, Proc. ICASE Workshop, Hampton/VA 1986, 124-150 (1989).
[For the entire collection see Zbl 0657.00012.]
We examine certain mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. Our principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing we also discuss useful algorithms. Because of space limitations we focus on the steady primitive variable formulation. Moreover, even within this narrow context, we concentrate on only one of the very many different known approaches.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs