Volume 14, Issue 4-5
Finite Element Method to Control the Domain Singularities of Poisson Equation Using the Stress Intensity Factor : Mixed Boundary Condition.

Int. J. Numer. Anal. Mod., 14 (2017), pp. 500-510

Published online: 2017-08

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• Abstract

In this article, we consider the Poisson equation on a polygonal domain with the domain singularity raised from the changed boundary conditions with the inner angle ω › \pi/2. The solution of the Poisson equation with such singularity has a singular decomposition: regular part plus singular part. The singular part is a linear combination of one or two singular functions. The coecients of the singular functions are usually called stress intensity factors and can be computed by the extraction formula. In  we introduced a new partial differential equation which has 'zero' stress intensity factor using this stress intensity factor, from whose solution we can obtain a very accurate solution of the original problem simply by adding singular part. Although the method in  works well for the Poisson problem with Dirichlet boundary condition, it does not give optimal results for the case with stronger singularity, for example, mixed boundary condition with bigger inner angle. In this paper we give a revised algorithm which gives optimal convergences for both cases.

• Keywords

Finite element singular function dual singular function stress intensity factor

• AMS Subject Headings

65F10 65N30

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-500, author = {Seokchan Kim and Hyung-Chun Lee}, title = {Finite Element Method to Control the Domain Singularities of Poisson Equation Using the Stress Intensity Factor : Mixed Boundary Condition.}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {500--510}, abstract = {In this article, we consider the Poisson equation on a polygonal domain with the domain singularity raised from the changed boundary conditions with the inner angle ω › \pi/2. The solution of the Poisson equation with such singularity has a singular decomposition: regular part plus singular part. The singular part is a linear combination of one or two singular functions. The coecients of the singular functions are usually called stress intensity factors and can be computed by the extraction formula. In  we introduced a new partial differential equation which has 'zero' stress intensity factor using this stress intensity factor, from whose solution we can obtain a very accurate solution of the original problem simply by adding singular part. Although the method in  works well for the Poisson problem with Dirichlet boundary condition, it does not give optimal results for the case with stronger singularity, for example, mixed boundary condition with bigger inner angle. In this paper we give a revised algorithm which gives optimal convergences for both cases.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10046.html} }
TY - JOUR T1 - Finite Element Method to Control the Domain Singularities of Poisson Equation Using the Stress Intensity Factor : Mixed Boundary Condition. AU - Seokchan Kim & Hyung-Chun Lee JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 500 EP - 510 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10046.html KW - Finite element KW - singular function KW - dual singular function KW - stress intensity factor AB - In this article, we consider the Poisson equation on a polygonal domain with the domain singularity raised from the changed boundary conditions with the inner angle ω › \pi/2. The solution of the Poisson equation with such singularity has a singular decomposition: regular part plus singular part. The singular part is a linear combination of one or two singular functions. The coecients of the singular functions are usually called stress intensity factors and can be computed by the extraction formula. In  we introduced a new partial differential equation which has 'zero' stress intensity factor using this stress intensity factor, from whose solution we can obtain a very accurate solution of the original problem simply by adding singular part. Although the method in  works well for the Poisson problem with Dirichlet boundary condition, it does not give optimal results for the case with stronger singularity, for example, mixed boundary condition with bigger inner angle. In this paper we give a revised algorithm which gives optimal convergences for both cases.
Seokchan Kim & Hyung-Chun Lee. (1970). Finite Element Method to Control the Domain Singularities of Poisson Equation Using the Stress Intensity Factor : Mixed Boundary Condition.. International Journal of Numerical Analysis and Modeling. 14 (4-5). 500-510. doi:
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