zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces. (English) Zbl 0635.76067
[For part VI see the review above (Zbl 0635.76066).] Symmetric finite element formulations are proposed for the primitive- variables form of the Stokes equations and shown to be convergent for any combination of pressure and velocity interpolations. Various boundary conditions, such as pressure, are accomodated.

76N10Compressible fluids, general
80A20Heat and mass transfer, heat flow
65Z05Applications of numerical analysis to physics
Full Text: DOI
[1] Arnold, D.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. anal. 19, 742-760 (1982) · Zbl 0482.65060
[2] Babuška, I.: Error bounds for finite element method. Numer. math. 16, 322-333 (1971) · Zbl 0214.42001
[3] Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO ser rouge anal. Numér. 2, 129-151 (1979)
[4] Carey, G. F.; Oden, J. T.: Finite elements: A second course II. (1983) · Zbl 0515.65075
[5] Franca, L. P.: New mixed finite element methods. Ph.d. thesis (1987)
[6] Franca, L. P.; Hughes, T. J. R.; Loula, A. F. D.; Miranda, I.: A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element method. Presented at the conference on the impact of mathematical analysis on the solution of engineering problems (1986) · Zbl 0656.73036
[7] Girault, V.; Raviart, P. A.: Finite element methods for Navier-Stokes equations. Theory and algorithms (1986) · Zbl 0585.65077
[8] Hellinger, E.: Der allgemeine ansatz der mechanik der kontinua. Encyclopädie der mathematischen wissenschaften 4, 602-694 (1914)
[9] Herrmann, L. R.: Elasticity equations for nearly incompressible materials by a variational theorem. Aiaa j. 3, 1896-1900 (1965)
[10] Hughes, T. J. R.: The finite element method: linear static and dynamic finite element analysis. (1987) · Zbl 0634.73056
[11] Hughes, T. J. R.; Franca, L. P.; Balestra, M.: A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. meths. Appl. mech. Engrg. 59, 85-99 (1986) · Zbl 0622.76077
[12] Jaunzemis, W.: Continuum mechanics. (1967) · Zbl 0173.52103
[13] Loula, A. F. D.; Franca, L. P.; Hughes, T. J. R.; Miranda, I.: Stability, convergence and accuracy of a new finite element method for the circular arch problem. Comput. meths. Appl. mech. Engrg. 63, 281-303 (1987) · Zbl 0607.73077
[14] Loula, A. F. D.; Hughes, T. J. R.; Franca, L. P.; Miranda, I.: Mixed Petrov-Galerkin method for the Timoshenko beam. Comput. meths. Appl. mech. Engrg. 63, 133-154 (1987) · Zbl 0607.73076
[15] Loula, A. F. D.; Miranda, I.; Hughes, T. J. R.; Franca, L. P.: A successful mixed formulation for axisymmetric shell analysis employing discontinuous stress fields of the same order as the displacement field. Fourth Brazilian symposium on piping and pressure vessels (1986)
[16] Pironneau, O.: Conditions aux limites sur la pression pour LES équations de Stokes et de Navier-Stokes. CR acad. Sc. Paris 303, No. 9, 403-406 (1986) · Zbl 0613.76028
[17] Reissner, E.: On a variational theorem in elasticity. J. math. Phys. 29, No. 2, 90-95 (1950) · Zbl 0039.40502
[18] Thomasset, F.: Implementation of finite element methods for Navier-Stokes equations. (1981) · Zbl 0475.76036