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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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Finite element technique for optimal pressure recovery from stream function formulation of viscous flows
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by M. E. Cayco and R. A. Nicolaides PDF
Math. Comp. 46 (1986), 371-377 Request permission

Abstract:

Following a general analysis of convergence for the finite element solution of the stream function formulation of the Navier-Stokes equation in bounded regions of the plane, an algorithm for pressure recovery is presented. This algorithm, which is easy to implement, is then analyzed and conditions ensuring optimality of the approximation are given. An application is made to a standard conforming cubic macroelement.
References
  • A. K. Aziz (ed.), The mathematical foundations of the finite element method with applications to partial differential equations, Academic Press, New York-London, 1972. MR 0347104
  • A. S. Benjamin & V. E. Denny, "On the convergence of numerical solutions for 2-D flows in a cavity at large Re," J. Comput. Phys., v. 33, 1979, pp. 340-358. P. L. Betts & V. Haroutunian, "A stream function finite element solution for two-dimensional natural convection," Finite Element Flow Analysis (T. Kawai, ed.), Univ. of Tokyo Press, 1982, pp. 279-288.
  • H. Blum and R. Rannacher, On the boundary value problem of the biharmonic operator on domains with angular corners, Math. Methods Appl. Sci. 2 (1980), no. 4, 556–581. MR 595625, DOI 10.1002/mma.1670020416
  • J. M. Boland and R. A. Nicolaides, Stability of finite elements under divergence constraints, SIAM J. Numer. Anal. 20 (1983), no. 4, 722–731. MR 708453, DOI 10.1137/0720048
  • Philippe G. Ciarlet, Metod konechnykh èlementov dlya èllipticheskikh zadach, “Mir”, Moscow, 1980 (Russian). Translated from the English by B. I. Kvasov. MR 608971
  • U. Ghia, K. N. Ghia & C. T. Shin, "High Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method," J. Comput. Phys., v. 48, 1982, pp. 387-411.
  • V. Girault and P.-A. Raviart, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Mathematics, vol. 749, Springer-Verlag, Berlin-New York, 1979. MR 548867
  • M. D. Olson & S.-Y. Tuann, "New finite element results for the square cavity," Comput. & Fluids, v. 7, 1979, pp. 123-135.
  • Shih Yu Tuann and Mervyn D. Olson, Review of computing methods for recirculating flows, J. Comput. Phys. 29 (1978), no. 1, 1–19. MR 510458, DOI 10.1016/0021-9991(78)90105-5
  • R. Schreiber and H. B. Keller, Spurious solutions in driven cavity calculations, J. Comput. Phys. 49 (1983), no. 1, 165–172. MR 694162, DOI 10.1016/0021-9991(83)90119-5
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Math. Comp. 46 (1986), 371-377
  • MSC: Primary 65N30; Secondary 76-08, 76D05
  • DOI: https://doi.org/10.1090/S0025-5718-1986-0829614-2
  • MathSciNet review: 829614