A novel efficient numerical solution of Laplace equation with mixed boundary conditions
Manki Cho · International Journal of Computer Mathematics · 2021
This paper describes a new type of method to solve Laplace equation subject to mixed boundary conditions in two-dimensional domains for electrostatics. The electric potential ϕ is represented by harmonic Steklov eigenfunctions, obtained from a certain Steklov eigenproblem. Error estimates for this method are provided in terms of given boundary data of solutions. The key idea of the method is that Steklov eigenfuncitons could construct the orthonormal basis of the space of solutions. Some results of computational simulations on polygonal domains are presented to support the effectiveness of the new method.