Abstract
The condition div \( \overrightarrow u = 0\) on a region Ω in Rn is approximated by finite differences. Grid functions ui,j. satisfying this condition form a vector space. Calculation of the dimension and calculation of a basis for this vector space are discussed. An illustrative example is included.
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References
R. Temam, Navier-Stokes Equations; Theory and Numerical Analysis, Elsevier North-Holland, New York, 1979.
K.E. Gustafson, Recent Progress on the Nonlinear Equations of Hartree-Fock, Concentration-Diffusion, Navier-Stokes, Proc. Conf. on Bifurcation Theory, Bielefeld, Oct. 1979, Applications of Nonlinear Analysis in the Physical Sciences, Pitman, London, to appear.
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© 1981 Plenum Press, New York
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Hartman, R.L., Gustafson, K. (1981). On the Dimension of a Finite Difference Approximation to Divergence-Free Vectors. In: Gustafson, K.E., Reinhardt, W.P. (eds) Quantum Mechanics in Mathematics, Chemistry, and Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3258-9_9
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DOI: https://doi.org/10.1007/978-1-4613-3258-9_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3260-2
Online ISBN: 978-1-4613-3258-9
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