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 mixed finite element method for elasticity in three dimensions. (English) Zbl 1125.74382
From the text: We describe a stable mixed finite element method for linear elasticity in three dimensions. This answers an assertion of D. N. Arnold [Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. I: Plenary lectures and ceremonies. Beijing: Higher Education Press. 137–157 (2002; Zbl 1023.65113)]: ‘Four decades of searching for mixed finite elements for elasticity, beginning in the 1960s, did not yield any stable elements with polynomial shape functions’. First D. N. Arnold and R. Winther [Numer. Math. 92, No. 3, 401–419 (2002; Zbl 1090.74051)] gave stable elements for a two-dimensional version of the problem, and remarked that the method of construction works in both two and three space dimensions, but for simplicity the discussion was limited to the two-dimensional case.

74S05Finite element methods in solid mechanics
74B05Classical linear elasticity
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
[1]Arnold, D. (2002). Differential complexes and numerical stability. In: Proceedings of the International Congress of Mathematicians, Vol.I (Beijing, 2002), 137–157, Higher Ed. Press, Beijing.
[2] · Zbl 1090.74051 · doi:10.1007/s002110100348
[3]Arnold, D., Awanou, G. and Winther, R. A family of mixed elements for elasticity in three dimensions. In preparation.