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Two different approaches for the treatment of boundary singularities
Author(s) -
Michavila F.,
Gavete L.,
Díez F.
Publication year - 1988
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.1690040307
Subject(s) - quadrilateral , mathematics , gravitational singularity , singularity , boundary (topology) , domain (mathematical analysis) , finite element method , mathematical analysis , singular point of a curve , point (geometry) , boundary value problem , singular boundary method , simplicity , element (criminal law) , boundary element method , geometry , law , structural engineering , philosophy , epistemology , political science , engineering
The finite element treatment of boundary singularities in elliptic problems has demanded that special techniques be developed. Many of these use some form of singular element in the neighborhood of a singular point. For a homogenous second‐order problem, defined in a domain with a polygonal boundary, we studied three cases with different singularity orders. Some results about the accuracy of the solution are presented. Numerical results have been obtained using Akin singular triangular elements with three and six nodes and quadrilateral elements having four and eight nodes. The behavior of the gradient in each of these elements is also analyzed. However, these elements are not completely satisfactory, so that an alternative technique using curved isoparametric elements is given here. The results obtained with the two methods are compared. Conclusions about numerical accuracy of each method, the order of integration and the simplicity of application are made.