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)
Some error estimates for the box method. (English) Zbl 0634.65105
The paper is devoted to the numerical analysis of the box method (called also box integration method, finite control volume method, or balance method) for solving self-adjoint, positive definite elliptic boundary value problems in plane regions. The analysis is made in terms of the Galerkin procedure known from the finite element method. For the Poisson equation under Dirichlet boundary conditions, the authors derive the estimate |u-u L ||u-u B |C|u-u L |, where |·| denotes the energy norm, and u, u B and u L are the exact solution, the approximate solution generated by the box method and the finite element solution obtained on the primary triangular mesh by means of linear elements, respectively. For the more general boundary value problem -div(au)+σu=f in Ω and u=0 on Ω with some zero-order term in the differential equation, the authors prove the estimate |u-u L ||u-u B |C(|u-u L |+u-u ¯ L L 2 (Ω) ), where u ¯ L =u L (x i )Φ ¯ i (x) and Φ ¯ i denotes the characteristic function of that box to which the vertex x i corresponds.
Reviewer: U.Langer

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35J25Second order elliptic equations, boundary value problems