Triangulation of planar regions by a finite element solution in the Galerkin form of the Dirichlet problem

The author has solved a new problem of triangulation of sufficiently regular bounded flat domain. The domain is represented by a combination of nonintersecting convex curvilinear subdomains with the number of angles from 3 to 6. Each subdomain is given a corresponding equivalent analog - an equilateral triangle or a convex polygon generated by it. The equivalent analog is transformed into a discrete one consisting of equilateral triangles. A conformal image of the discrete analog on the domain under analysis is made by the FEA solution in Galyorkin form of the boundary value Dirichlet problem using Laplacian. The result of the imaging is a discrete model of the domain under investigation with the triangular elements being close to equilateral.