Pitkäranta, Juhani On a mixed finite element method for the Stokes problem in \(R^ 3\). (English) Zbl 0488.76039 RAIRO, Anal. Numér. 16, 275-291 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents MSC: 76D07 Stokes and related (Oseen, etc.) flows 76M99 Basic methods in fluid mechanics 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:mixed element; rectangular domain; three dimensional; stability for pressure; superapproximation properties for velocities; regular mesh PDF BibTeX XML Cite \textit{J. Pitkäranta}, RAIRO, Anal. Numér. 16, 275--291 (1982; Zbl 0488.76039) Full Text: DOI EuDML References: [1] I BABUSKA, Error bounds for finite element methods, Numer Math 16, 1971, pp 322-333. Zbl0214.42001 MR288971 · Zbl 0214.42001 · doi:10.1007/BF02165003 · eudml:132037 [2] F BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, RAIRO 8-R2, 1974, pp 129-151. Zbl0338.90047 MR365287 · Zbl 0338.90047 · eudml:193255 [3] P CIARLET, The Finite Element Method for Elliptic Problems, North Holland, 1978. Zbl0383.65058 MR520174 · Zbl 0383.65058 [4] B DALY, F HARLOW, J SAHNNON and J WELCH, The MAC method, Technical report LA-3425, Los Alamos Scientific Laboratory, 1965. [5] V GIRAUTL and P-A RAVIART, Finite Element Approximation of the Navter-Stokes Equations, Lecture Notes in Mathematics, Springer, Berlin, 1979. Zbl0413.65081 MR540128 · Zbl 0413.65081 · doi:10.1007/BFb0063447 [6] P GRISVARD, Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, in Numerical Solution of Partial Differential Equations III, ed B Hubbard, Academic Press, New York, 1976. Zbl0361.35022 MR466912 · Zbl 0361.35022 [7] C JOHNSON and J PITKARANTA, Analysis of some mixed finite element methods related to reduced integration, Preprint, Chalmers University of Technology, 1980. Zbl0482.65058 MR645657 · Zbl 0482.65058 · doi:10.2307/2007276 [8] D ted to red and T HUGUES, Mixed finite element methods reduced and selective integration techniques a unification of concepts, Comp Meth Appl Mech Engng 15, 1978, pp 63-81. Zbl0381.73075 · Zbl 0381.73075 · doi:10.1016/0045-7825(78)90005-1 [9] H MELZER and R RANNACHER, Spannungskonzentrationen in der Eckpunkten der vertikalen belasteten Kirchoffschen Platte, Preprint, 1979, Universitat Bonn. [10] R SANI, P GRESHO, R LEE and GRIFFITHS, The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-stokes equations, Preprint, 1980, Lawrence Livermore Laboratory. Zbl0461.76021 · Zbl 0461.76021 · doi:10.1002/fld.1650010104 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.