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), 371377
MSC:
Primary 65N30; Secondary 7608, 76D05
MathSciNet review:
829614
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Following a general analysis of convergence for the finite element solution of the stream function formulation of the NavierStokes 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]
A.
K. Aziz (ed.), The mathematical foundations of the finite element
method with applications to partial differential equations, Academic
Press, New YorkLondon, 1972. MR 0347104
(49 #11824)
 [2]
A. S. Benjamin & V. E. Denny, "On the convergence of numerical solutions for 2D flows in a cavity at large Re," J. Comput. Phys., v. 33, 1979, pp. 340358.
 [3]
P. L. Betts & V. Haroutunian, "A stream function finite element solution for twodimensional natural convection," Finite Element Flow Analysis (T. Kawai, ed.), Univ. of Tokyo Press, 1982, pp. 279288.
 [4]
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
(82a:35022), http://dx.doi.org/10.1002/mma.1670020416
 [5]
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
(85e:65046), http://dx.doi.org/10.1137/0720048
 [6]
Philippe
G. Ciarlet, Metod konechnykh elementov dlya ellipticheskikh
zadach, “Mir”, Moscow, 1980 (Russian). Translated from the
English by B. I. Kvasov. MR 608971
(82c:65068)
 [7]
U. Ghia, K. N. Ghia & C. T. Shin, "High Re solutions for incompressible flow using the NavierStokes equations and a multigrid method," J. Comput. Phys., v. 48, 1982, pp. 387411.
 [8]
V.
Girault and P.A.
Raviart, Finite element approximation of the NavierStokes
equations, Lecture Notes in Mathematics, vol. 749,
SpringerVerlag, BerlinNew 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. 123135.
 [10]
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
(80g:76023), http://dx.doi.org/10.1016/00219991(78)901055
 [11]
R.
Schreiber and H.
B. Keller, Spurious solutions in driven cavity calculations,
J. Comput. Phys. 49 (1983), no. 1, 165–172. MR 694162
(85a:76018), http://dx.doi.org/10.1016/00219991(83)901195
 [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 2D flows in a cavity at large Re," J. Comput. Phys., v. 33, 1979, pp. 340358.
 [3]
 P. L. Betts & V. Haroutunian, "A stream function finite element solution for twodimensional natural convection," Finite Element Flow Analysis (T. Kawai, ed.), Univ. of Tokyo Press, 1982, pp. 279288.
 [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. 556581. 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. 722731. MR 708453 (85e:65046)
 [6]
 P. G. Ciarlet, The Finite Element Method for Elliptic Problems, NorthHolland, Amsterdam, 1980. MR 608971 (82c:65068)
 [7]
 U. Ghia, K. N. Ghia & C. T. Shin, "High Re solutions for incompressible flow using the NavierStokes equations and a multigrid method," J. Comput. Phys., v. 48, 1982, pp. 387411.
 [8]
 V. Girault & P.A. Raviart, Finite Element Approximations of the NavierStokes Equations, Lecture Notes in Math., vol. 749, SpringerVerlag, 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. 123135.
 [10]
 M. D. Olson & S.Y. Tuann, "Review of computing methods for recirculating flows," J. Comput. Phys., v. 29, 1978, pp. 119. MR 510458 (80g:76023)
 [11]
 R. Schreiber & H. B. Keller, "Driven cavity flows by efficient numerical techniques," J. Comput. Phys., v. 49, 1983, pp. 310333. MR 694162 (85a:76018)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65N30,
7608,
76D05
Retrieve articles in all journals
with MSC:
65N30,
7608,
76D05
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608296142
PII:
S 00255718(1986)08296142
Article copyright:
© Copyright 1986
American Mathematical Society
