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)
Hanging nodes and XFEM. (English) Zbl 1216.74020
Summary: This paper investigates two approaches for the handling of hanging nodes in the framework of extended finite element methods (XFEM). Allowing for hanging nodes, locally refined meshes may be easily generated to improve the resolution of general, i.e. model-independent, steep gradients in the problem under consideration. Hence, a combination of these meshes with XFEM facilitates an appropriate modeling of jumps and kinks within elements that interact with steep gradients. Examples for such an interaction are, e.g. found in stress fields near crack fronts or in boundary layers near internal interfaces between two fluids. The two approaches for XFEM based on locally refined meshes with hanging nodes basically differ in whether (enriched) degrees of freedom are associated with the hanging nodes. Both approaches are applied to problems in linear elasticity and incompressible flows.

74S05Finite element methods in solid mechanics
76M10Finite element methods (fluid mechanics)
74B05Classical linear elasticity
76D05Navier-Stokes equations (fluid dynamics)
Full Text: DOI