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Mixed finite element approximation of the vector potential. (English) Zbl 0596.76073
We consider a mixed finite element approximation of the three-dimensional vector potential, which plays an important rôle in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows. The central point of our approach is a saddle- point formulation of the essential boundary conditions.
In particular, this avoids the wellknown Babuška paradox when approximating smooth domains by polyhedrons. Using piecewise linear/piecewise constant elements for the vector potential/ the boundary terms, we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem.

76H05 Transonic flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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