Solution of two-dimensional Poisson problems in quadrilateral domains using transfinite Coons interpolation

摘要

This paper proposes a global approximation method to solve elliptic boundary value Poisson problems in arbitrary shaped 2-D domains. Using transfinite interpolation, a symmetric finite element formulation is derived for degrees of freedom arranged mostly along the boundary of the domain. In cases where both Dirichlet and Neumann boundary conditions occur, the numerical solution is based on bivariate Coons interpolation using the boundary only. Furthermore, in case of only Dirichlet boundary conditions and no existing axes of symmetry, it is proposed to use at least one internal point and apply transfinite interpolation. The theory is sustained by five numerical examples applied to domains of square, circular and elliptic shape.