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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in $\textbf {R}^ 3$
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by V. Girault PDF
Math. Comp. 51 (1988), 55-74 Request permission


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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 55-74
  • MSC: Primary 65N30; Secondary 76-08, 76D05
  • DOI:
  • MathSciNet review: 942143