A harmonic polynomial method with a regularization strategy for the boundary value problems of Laplace's equation. (May 2018) - Zhang, Deyue; Sun, Fenglin; Lu, Linyan; Guo, Yukun
Abstract: This paper concerns a boundary value problem of Laplace's equation, which is solved by determining the unknown coefficients in the expansion of harmonic polynomials. A regularization method is proposed to tackle the resulting ill-posed linear system. The stability and convergence results are provided and a validating numerical experiment is presented.