Ye, Xiu Superconvergence of nonconforming finite element method for the Stokes equations. (English) Zbl 1003.65121 Numer. Methods Partial Differ. Equations 18, No. 2, 143-154 (2002). The numerical solution of the Stokes problem with the aid of the nonconforming finite element method is considered. The superconvergence is obtained using a least-squares surface fitting method proposed by J. Wang for the standard Galerkin method [J. Math. Study 33, No. 3, 229-243 (2000; Zbl 0987.65108)]. The regularly of the solution is assumed. The obtained results are applicable for any pairs of nonconforming stable finite elements. Two examples of elements (Crousier-Raviart and Douglas quadrilateral) are presented. Reviewer: Vit Dolejsi (Praha) Cited in 32 Documents MSC: 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 76D07 Stokes and related (Oseen, etc.) flows 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35Q30 Navier-Stokes equations Keywords:Stokes equations; nonconforming finite element method; superconvergence; least-squares surface fitting method Citations:Zbl 0987.65108 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] and A rectangle test for the Stokes problem, Proc. System Science and Systems Engineering, 1991, Great Hall (H.K.) Culture Publishing, pp 236-237. [2] and Global superconvergence for rectangular elements for the Stokes problem, Proc. System Science and Systems Engineering, 1991, Great Hall (H. K.) Culture Publishing, pp 371-376. [3] and Superconvergence of finite element approximations for the Stokes problem by least squares surface fitting, submitted. [4] Douglas, Calcolo 26 pp 121– (1989) [5] Ewing, SIAM J Numer Anal [6] Wahlbin, Lect Notes Math 1605 (1995) · Zbl 0826.65092 · doi:10.1007/BFb0096835 [7] Schatz, SIAM J Numer Anal 33 pp 505– (1996) [8] and Superconvergence of the gradients in the finite element method for some elliptic and parabolic problems, Variational-difference methods in mathematical physics, Part II, Proc. of the Fifth International Conference, 1984, Moscow, pp 13-25. [9] Zienkiewicz, Int J Numer Meth Eng 33 pp 1331– (1992) [10] Zienkiewicz, Int J Numer Meth Eng 33 pp 1365– (1992) [11] Li, Numer Meth Part Diff Eq 15 pp 151– (1999) [12] Crouzeix, RAIRO R3 pp 33– (1973) [13] and Finite element methods for the Navier-Stokes equations: theory and algorithms, Springer, Berlin, 1986. · Zbl 0585.65077 · doi:10.1007/978-3-642-61623-5 [14] Wang, J Math Study [15] The finite element method for elliptic problems, North-Holland, New York, 1978. [16] Douglas, Math Model Numer Anal 33 pp 747– (1999) [17] Cai, Calcolo 36 pp 215– (1999) [18] Zhang, Computer Meth Appl Mech Eng 163 pp 159– (1998) [19] Zlamal, Math Comp 32 pp 663– (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.