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-level Picard and modified Picard methods for the Navier-Stokes equations. (English) Zbl 0828.76017
Iterative methods of Picard type for the Navier-Stokes equations are known to converge only for quite small Reynolds numbers. However, we study methods involving just one such iteration at general Reynolds numbers. For the initial approximation a coarse mesh of width h 0 is used. The corrected approximation is computed by just one Picard or modified Picard step on a fine mesh of width h 1 . For example, h 1 may be of order O(h 0 2 ) when linear velocity elements are used. The resulting method requires the solution of a (small) system of nonlinear equations on the coarse mesh and only one (larger) linear system on the fine mesh. This two-level Picard method is proven to converge for fixed Reynolds number as h0. Further, the fine mesh solution satisfies a quasi-optimal error bound.
MSC:
76D05Navier-Stokes equations (fluid dynamics)
76M10Finite element methods (fluid mechanics)
65H10Systems of nonlinear equations (numerical methods)