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 Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces. (English) Zbl 1143.35022
The authors propose a second-order accurate method for the solution of elliptic equations with variable coefficients and discontinuities across an embedded interface. The interface is represented by a level set approach. In contrast to existing methods in the literature the authors exploit a finite volume approach on Cartesian grids using ideas from finite element methods in reconstructing the solution within grid cells. The authors present a piecewise bilinear finite element for irregular cut cells taking into account known jump conditions of the solution and the normal gradient across the interface. They resolve singularities arising from the bilinear ansatz itself and the position of the interface relative to the grid by a two-step asymptotic approach. The method achieves second-order of accuracy in $L^\infty$ and $L^2$ norms.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
Software:
hypre
WorldCat.org
Full Text: DOI