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)
An efficient method for subtracting off singularities at corners for Laplace’s equation. (English) Zbl 0657.65129

The author derives a formula for the coefficients of an asymptotic expansion of the solution of Laplace’s equation near a singularity like a corner or a point of change of type of the boundary conditions. The approach is then as follows: The solution is approximated by discretization, the coefficients of a finite part of the series are found (by computing certain line integrals of the solution along a part of a circle) and the series is subtracted (which means essentially modifying the boundary conditions). This process is repeated iteratively. Finally, the series is added to the modified solution.

Computational results are given for a number of problems. A comparison with the adaptive multigrid code PLTMG of R. E. Bank [PLTMG user’s guide: Dept. of Math., University of California at San Diego, CA (1985)] results are better by one-two orders of accuracy.

Reviewer: G.Stoyan
MSC:
65Z05Applications of numerical analysis to physics
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation