FINITE ELEMENT SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATION WITH MULTIPLE CONCAVE CORNERS

다국어 초록 (Multilingual Abstract)

In [8] they introduced a new nite element method foraccurate numerical solutions of Poisson equations with corner sin-gularities. They consider the Poisson equations with homogeneousDirichlet boundary condition with one corner singularity at the ori-gin, and compute the nite element solution using standard FEMand use the extraction formula to compute the stress intensity fac-tor, then pose a PDE with a regular solution by imposing the non-homogeneous boundary condition using the computed stress inten-sity factor, which converges with optimal speed. From the solutionthey could get an accurate solution just by adding the singular part.
This approach uses the polar coordinate and the cut-o function tocontrol the singularity and the boundary condition.
In this paper we consider Poisson equations with multiple sin-gular points, which involves di erent cut-o functions which mightoverlaps together and shows the way of cording in FreeFEM++ tocontrol the singular functions and cut-o functions with numericalexperiments.

참고문헌 (Reference)

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9 S. Kim, "A nite element method for computing accurate solutions for Poisson equations with corner singularities using the stress intensity factor" 71 : 2330-2337, 2016