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Aris, R. (1962), Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, p. 129.
Byrne, G., Hindmarsh, A., Jackson, K. and Brown, H. (1977), "A Comparison of Two ODE Codes: GEAR and EPISODE", Comp. and Chem. Eng., V. 1, pp. 133–147.
Gresho, P. and Lee, R. (1979), "Don't Suppress the Wiggles — They're Telling You Something!", ASME Symposium on Finite Element Methods for Convection-Dominated Flows, Winter Annual ASME Meeting, NY, December (1979).
Gresho, P., Lee, R., and Sani, R. (1980a), "On the Time-Dependent FEM Solution of the Incompressible Navier-Stokes Equations in Two-and Three-Dimensions," in Recent Advances in Numerical Methods in Fluids, Pineridge Press, Ltd., Swansea, U. K. (to appear).
Gresho, P., Lee, R., Chan, S. and Leone, J. (1980b), "A New Finite Element for Incompressible or Boussinesq Fluids," Proc. Third International Conference on Finite Elements in Flow Problems, Banff, Canada (to appear).
Hindmarsh, A. (1972), "Construction of Mathematical Software, Part III: The Control of Error in the Gear Package for Ordinary Differential Equations," Lawrence Livermore Laboratory Report UCID-30050, Part 3, Livermore, CA.
Hood, P. (1976), "Frontal Solution method for Unsymmetric Matrices," Int. J. for Num. Meth. Eng., 10, pp. 379–399.
Lee, R., Gresho, P., Chan, S., and Sani, R. (1980), "A Comparison of Several Conservative Forms for Finite Element Formulations of the Incompressible Navier-Stokes or Boussinesq Equations," Proc. Third International Conference on Finite Elements in Flow Problems, Banff, Canada (to appear).
Leone, J. and Gresho, P. (1979), "Finite Element Simulations of Steady, Two-Dimensional Viscous Incompressible Flow Over a Step," submitted to J. Comp. Phys.
Marshall, R., Heinrich, J., and Zienkiewicz, O. (1978), "Natural Convection in a Square Enclosure by a Finite-Element, Penalty Function Method Using Primitive Fluid Variables," Num. Heat Transfer, 1, pp. 315–330.
Olson, M. (1977), "Comparison of Various Finite Element Solution Methods for the Navier-Stokes Equations," in Finite Elements in Water Resources, Pentech Press, London, p. 4.185.
Sani, R., Gresho, P., and Lee, R. (1980), "On the Spurious Pressures Generated by Certain FEM Solutions of the Incompressible Navier-Stokes Equations," Proc. Third International Conference on Finite Elements in Flow Problems, Banff, Canada (to appear).
Schlichting, H. (1960), Boundary Layer Theory, McGraw-Hill, N. Y.
Shampine, L. and Gordon, M. (1975), Computer Solution of Ordinary Differential Equations: The Initial Value Problem, W. Freeman and Company, San Francisco, CA.
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Gresho, P.M., Lee, R.L., Chan, S.T., Sani, R.L. (1980). Solution of the time-dependent incompressible Navier-Stokes and Boussinesq equations using the Galerkin finite element method. In: Rautmann, R. (eds) Approximation Methods for Navier-Stokes Problems. Lecture Notes in Mathematics, vol 771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086908
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DOI: https://doi.org/10.1007/BFb0086908
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