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Finite element treatment of boundary singularities by augmentation with non‐exact singular functions
Author(s) -
Beagles A. E.,
Whiteman J. R.
Publication year - 1986
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690020203
Subject(s) - mathematics , gravitational singularity , reentrancy , finite element method , poisson distribution , singular solution , mathematical analysis , singular function , function (biology) , boundary value problem , poisson's equation , boundary (topology) , singular integral , integral equation , evolutionary biology , biology , statistics , physics , computer science , thermodynamics , programming language
Abstract A two‐dimensional Poisson problem which contains both an interface and a reentrant corner is considered. For this problem the singular form of the solution at the reentrant corner is not known explicitly, with the result that a ( nonexact ) approximation to the singular form has to be calculated. The finite element method is applied to the Poisson problem, with the test and trial function spaces augmented with the nonexact singular functions. An error analysis for the nonexact augmentation is presented.