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)
A two-grid discretization scheme for eigenvalue problems. (English) Zbl 0959.65119

A two-grid discretization technique is presented for solving linear eigenvalue problems posed in variational form,

a(u,v)=λb(u,v)forallvX·

Here, X denotes a real Hilbert space, and a(,) and b(,) are symmetric and positive bilinear forms such that the problem exhibits a point spectrum 0<λ 1 λ 2 . Two linear finite element subspaces S H S h X are introduced which are defined on a coarse grid T H and a refined grid T h , respectively. Given on the coarse grid an approximate eigensolution u H S H , λ H R 1 , then u h S h , λR 1 is defined by a(u h ,v)=λ H b(u H ,v) for all vs h together with λ h =a(u h ,u h )/b(u h ,u h ). Asymptotic error estimates in terms of H and h are presented. The technique is illustrated by simple numerical experiments for the first Laplace eigenvalue problem on the unit square.


MSC:
65N25Numerical methods for eigenvalue problems (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N15Error bounds (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35P15Estimation of eigenvalues and upper and lower bounds for PD operators