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The Numerical Methods for Oscillating Singularities in Elliptic Boundary Value Problems

โœ Scribed by Hae-Soo Oh; Hoonjoo Kim; Sung-Jin Lee

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
278 KB
Volume
170
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

The singularities near the crack tips of homogeneous materials are monotone of type r ฮฑ and r ฮฑ log ฮด r (depending on the boundary conditions along nonsmooth domains). However, the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type r ฮฑ sin(ฮต log r ). The method of auxiliary mapping (MAM), introduced by Babuลกka and Oh, was proven to be successful in dealing with r ฮฑ type singularities. However, the effectiveness of MAM is reduced in handling oscillating singularities. This paper deals with oscillating singularities as well as the monotone singularities by extending MAM through introducing the power auxiliary mapping and the exponential auxiliary mapping.

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## Abstract The method of auxiliary mapping (MAM), introduced by Babuลกka and Oh, was proven to be very successful in dealing with monotone singularities arising in twoโ€dimensional problems. In this article, in the framework of the __p__โ€version of FEM, MAM is presented for oneโ€dimensional elliptic