Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Analysis of the finite element variable penalty method for Stokes equations


Authors: Haroon Kheshgi and Mitchell Luskin
Journal: Math. Comp. 45 (1985), 347-363
MSC: Primary 65N30; Secondary 76D07
DOI: https://doi.org/10.1090/S0025-5718-1985-0804928-X
MathSciNet review: 804928
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give an error analysis of the finite element variable penalty method for Stokes equations. It is shown that the variable penalty method is of higher order than the standard penalty method.


References [Enhancements On Off] (What's this?)

  • [1] J. Bramble & A. Schatz, "Higher order local accuracy by averaging in the finite element method." Math. Comp., v. 31, 1977, pp. 94-111. MR 0431744 (55:4739)
  • [2] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 0520174 (58:25001)
  • [3] V. Girault & P.-A. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Math., Vol. 749, Springer-Verlag, Berlin, 1979. MR 548867 (83b:65122)
  • [4] T. Hughes, W. Liu & A. Brooks, "Finite element analysis of incompressible viscous flows by the penalty function formulation," J. Comput. Phys., v. 30, 1979, pp. 1-60. MR 524162 (80b:76008)
  • [5] H. Kheshgi & M. Luskin, "On the variable sign penalty approximation of the Navier-Stokes equation," Nonlinear Partial Differential Equations (Joel Smoller, ed.), Contemporary Mathematics, Vol. 17, Amer. Math. Soc., Providence, R. I., 1983. MR 706090 (84m:76039)
  • [6] H. Kheshgi & L. Scriven, "Finite element analysis of incompressible viscous flow by a variable penalty function method," Penalty-Finite Element Methods in Mechanics (J. N. Reddy, ed.), AMD-Vol. 51, A. S. M. E., New York, 1982.
  • [7] H. Kheshgi & L. Scriven, "Variable penalty method for finite element analysis of incompressible Stokes flow," Internat. J. Numer. Methods Fluids. (To appear.) MR 805856 (86j:76002)
  • [8] J. Nitsche & A. Schatz, "Interior estimates for Ritz-Galerkin methods," Math. Comp., v. 28, 1974, pp. 937-958. MR 0373325 (51:9525)
  • [9] R. Temam, Navier-Stokes Equations, 2nd ed., North-Holland, Amsterdam, 1979. MR 603444 (82b:35133)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30, 76D07

Retrieve articles in all journals with MSC: 65N30, 76D07


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1985-0804928-X
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society