Spline-interpolation solution of 3D Dirichlet problem for a certain class of solids
The authors present a spline-interpolation approximate solution of the Dirichlet problem for the Laplace equation in axisymmetric domains. The spline-interpolation method is the analogue of the finite element method where instead of the boundary nodes one considers the closed boundary curves and introduces the cells as the layers between two parallel planes. So, the 3D problem is reduced to a sequence of 2D Dirichlet problems. The main advantage of the spline-interpolation solution is its continuity in the whole domain up to the boundary. An error estimate of the problem is obtained.The spline-interpolation solution presented in the paper is also applied to the Dirichlet problem for a cylinder or a cone with the section which is the known conformal map of the unit disc. Some examples illustrate the theory.
scientific article; zbMATH DE number 6251138