Steklov Expansion Method for Regularized Harmonic Boundary Value Problems. (13th November 2020) - Cho, Manki
Abstract: A new type of meshless method is proposed in this paper to solve regularized Laplacian boundary value problems of the form L u : = r 2 u − Δ u ≡ 0 . In this method, solving the Laplacian boundary value problem is starting from finding regularized Steklov eigenpairs which could provide the orthonormal basis of the space of solutions. The solutions are represented by orthogonal regularized Steklov eigenfunctions. Error bounds of Steklov approximations are provided in terms of the traces spaces of solutions. When rectangular domains are considered, explicit formulas for the regularized Steklov eigenpairs are provided. Some numerical experiments are presented to support the efficiency and accuracy of the new method.