Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in $\textbf {R}^ 3$
Author:
V. Girault
Journal:
Math. Comp. 51 (1988), 55-74
MSC:
Primary 65N30; Secondary 76-08, 76D05
DOI:
https://doi.org/10.1090/S0025-5718-1988-0942143-2
MathSciNet review:
942143
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Abstract: This paper is devoted to the steady state, incompressible Navier-Stokes equations with nonstandard boundary conditions of the form ${\mathbf {u}} \cdot {\mathbf {n}} = 0$, $\mathbf {curl}\;{\mathbf {u}} \times {\mathbf {n}} = {\mathbf {0}}$, either on the entire boundary or mixed with the standard boundary condition ${\mathbf {u}} = {\mathbf {0}}$ on part of the boundary. The problem is expressed in terms of vector potential, vorticity and pressure. The vorticity and vector potential are approximated with curl-conforming finite elements and the pressure with standard continuous finite elements. The error estimates yield nearly optimal results for the purely nonstandard problem.
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© Copyright 1988
American Mathematical Society