Finite element technique for optimal pressure recovery from stream function formulation of viscous flows

Authors:
M. E. Cayco and R. A. Nicolaides

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

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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.

**[1]**I. Babuška & A. K. Aziz,*The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations*, Academic Press, New York, 1972. MR**0347104 (49:11824)****[2]**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.**[3]**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.**[4]**H. Blum & R. Rannacher, "On the boundary value problem of the biharmonic operator on domains with angular corners,"*Math. Methods Appl. Sci.*, v. 2, 1980, pp. 556-581. MR**595625 (82a:35022)****[5]**J. M. Boland & R. A. Nicolaides, "Stability of finite elements under divergence constraints,"*SIAM J. Numer. Anal.*, v. 20, no. 4, 1983, pp. 722-731. MR**708453 (85e:65046)****[6]**P. G. Ciarlet,*The Finite Element Method for Elliptic Problems*, North-Holland, Amsterdam, 1980. MR**608971 (82c:65068)****[7]**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.**[8]**V. Girault & P.-A. Raviart,*Finite Element Approximations of the Navier-Stokes Equations*, Lecture Notes in Math., vol. 749, Springer-Verlag, New York, 1979. MR**548867 (83b:65122)****[9]**M. D. Olson & S.-Y. Tuann, "New finite element results for the square cavity,"*Comput. & Fluids*, v. 7, 1979, pp. 123-135.**[10]**M. D. Olson & S.-Y. Tuann, "Review of computing methods for recirculating flows,"*J. Comput. Phys.*, v. 29, 1978, pp. 1-19. MR**510458 (80g:76023)****[11]**R. Schreiber & H. B. Keller, "Driven cavity flows by efficient numerical techniques,"*J. Comput. Phys.*, v. 49, 1983, pp. 310-333. MR**694162 (85a:76018)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829614-2

Article copyright:
© Copyright 1986
American Mathematical Society