zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Two families of mixed finite elements for second order elliptic problems. (English) Zbl 0599.65072
Two families of mixed finite elements are introduced in order to deal with second order elliptic problems. The asymptotic errors are the same as in the usual Raviart-Thomas-Nedelec spaces, but the new spaces have substantially smaller dimension; this fact should imply a greater computational efficiency, because the discretizations with the new spaces lead to algebraic systems of smaller order.
Reviewer: J.P.Milaszewicz

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
References:
[1]Arnold, D.N. Brezzi, F.: Mixed and nonconforming finite element methods: Implementation, postprocessing, and error estimates. RAIRO. (To appear)
[2]Brezzi, F.: On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO, Anal. numér.2, 129-151 (1974)
[3]Brezzi, F., Douglas, Jr., J., Marini, L.D.: Variable degree mixed methods for second order elliptic problems. (To appear)
[4]Brezzi, F., Douglas, Jr., J., Marini, L.D.: Recent results on mixed methods for second order elliptic problems. (To appear)
[5]Douglas, Jr., J., Roberts, J.E.: Mixed finite element methods for second order elliptic problems. Mathemática Applicada e Computacional1, 91-103 (1982)
[6]Douglas, Jr., J., Roberts, J.E.: Global estimates for mixed methods for second order elliptic equations. Math. Comput.44, 39-52 (1985) · doi:10.1090/S0025-5718-1985-0771029-9
[7]Dupont, T., Scott, R.: Polynomial approximation of functions in Sobolev space, Math. Comput.34, 441-463 (1980) · doi:10.1090/S0025-5718-1980-0559195-7
[8]Fraeijs de Veubeke, B.X.: Displacement and equilibrium models in the finite element method. Stress analysis, O.C. Zienkiewicz, G. Holister, eds. New York: Wiley 1965
[9]Fraeijs de Veubeke, B.X.: Stress function approach, World Congress on the Finite Element Method in Structural Mechanics. Bournemouth, 1975
[10]Handbook of mathematical functions, M. Abromowitz, I. Stegun, eds., Chapter 22 (O.W. Hochstrasser)
[11]Johnson, C. Thomée, V.: Error estimates for some mixed finite element methods for parabolic type problems. RAIRO, Anal. numér.15, 41-78 (1981)
[12]Nedelec, J.C.: Mixed finite elements in ?3. Numer. Math.35, 315-341 (1980) · Zbl 0419.65069 · doi:10.1007/BF01396415
[13]Nitsche, J.: Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg36, 9-15 (1970/1971) · Zbl 0229.65079 · doi:10.1007/BF02995904
[14]Raviart, P.A., Thomas, J.M.: A mixed finite element method for 2nd order elliptic problems. Mathematical aspects of the finite element method. Lecture Notes in Mathematics, Vol. 606. Berlin-Heidelberg-New York: Springer 1977