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 coecients of the singular functions are usually called stress intensity factors and can be
computed by the extraction formula. In [11] 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 [11] 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.