The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities

Oh, Hae‐Soo; Babuška, Ivo

doi:10.1016/s0021-9991(95)90017-9

Cited by 48 publications

(29 citation statements)

References 31 publications

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“…However, Table I shows that the results in "sub-optimal(under-sized)" is better than those in "super-optimal(over-sized)," because 1/0.66 is closer to the optimal size of the mapping. As mentioned before, these results of MAM are different from those of MAM for two-dimensional elasticity problems ( [17]). 4.…”

Section: Numerical Resultsmentioning

confidence: 61%

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Numerical methods and error analysis for one dimensional elliptic problems containing singularities

Kim

Lee

2003

Numerical Methods Partial

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The method of auxiliary mapping (MAM), introduced by Babuška and Oh, was proven to be very successful in dealing with monotone singularities arising in two-dimensional problems. In this article, in the framework of the p-version of FEM, MAM is presented for one-dimensional elliptic boundary value problems containing singularities. Moreover, in order to show the effectiveness of MAM, a detailed proof of an error estimate is also presented, which gives a sharp error bound of MAM.

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Section: Numerical Resultsmentioning

confidence: 61%

“…MAM was generalized to deal with 3D singularities (the vertex singularities, the edge singularities, and the edge-vertex combined singularities) ( [28]) as well as 2D singularities ( [17]). However, a rigorous mathematical analysis of extending MAM in the p-FEM to higher dimensions is under investigation.…”

Section: Discussionmentioning

confidence: 99%

Numerical methods and error analysis for one dimensional elliptic problems containing singularities

Kim

Lee

2003

Numerical Methods Partial

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“…Since g( x) ϭ 0 on ⍀ c , Ꮽ(u, u) has the weight e Ϫg( x)͉x͉ ϭ 1 on ⍀ c . It is known [23,26] that ʈu fe Ϫ u ex ʈ E 2 ϭ ͉ᐁ(u fe ) Ϫ ᐁ(u ex )͉, provided that all boundary conditions are either homogeneous Dirichlet or arbitrary traction boundary conditions. In this section, by the Relative Error (%) in Energy Norm, we mean…”

Section: Numerical Resultsmentioning

confidence: 99%

The weighted Ritz‐Galerkin method for elliptic boundary value problems on unbounded domains

Jang

Jou

2003

Numerical Methods Partial

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Recently Babuska-Oh introduced the method of auxiliary mapping (MAM) which efficiently handles elliptic boundary value problems containing singularities. In this paper, a special weighted residue method, the Weighted Ritz-Galerkin Method (WRGM), is investigated by introducing special weight functions. Together with this method, MAM is modified to yield highly accurate finite element solutions to general elliptic boundary value problems on the exterior of bounded domains at low cost.

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“…references cited in Reference [21]. There are other methodologies as well, including the DtN approach [21][22][23] and the method of auxiliary mapping [24]. Another aspect of FCP is the way of dealing with the constantly changing geometry due to the crack growth.…”

Section: Introductionmentioning

confidence: 99%

An adaptive finite element framework for fatigue crack propagation

Givoli

Zusman

2002

Numerical Meth Engineering

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SUMMARYA new ÿnite element (FE) framework for fatigue crack propagation (FCP) analysis is proposed. This framework combines the simplicity of standard industrial FCP analysis with the generality and accuracy of a full FE analysis and can be implemented on a small computer by combining standard existing computational tools. In this way it constitutes an attractive alternative to existing approaches. The framework is based on linear elastic fracture mechanics and on FE mesh adaptation. Some novel features are introduced in several of its steps in order to make it e cient and at the same time reasonably accurate. Various computational aspects of the scheme are discussed. A few two-dimensional numerical examples involving FCP in thin sheets under plane-stress conditions are presented to demonstrate the performance of the framework. Some of the numerical results are compared to those of laboratory experiments.

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The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities

Cited by 48 publications

References 31 publications

Numerical methods and error analysis for one dimensional elliptic problems containing singularities

Numerical methods and error analysis for one dimensional elliptic problems containing singularities

The weighted Ritz‐Galerkin method for elliptic boundary value problems on unbounded domains

An adaptive finite element framework for fatigue crack propagation

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