Steklov approximations of harmonic boundary value problems on planar regions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:321

Article

Auchmuty, Giles¹  Cho, Manki² 

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Rochester Inst Technol, Sch Math Sci, Rochester, NY 14623 USA

关键词: Harmonic functions;    Steklov eigenfunctions;    Boundary value problems;    Harmonic approximation;   

DOI  :  10.1016/j.cam.2017.02.034

来源: Elsevier

【 摘 要 】

Error estimates for approximations of solutions of Laplace's equation with Dirichlet, Robin or Neumann boundary value conditions are described. The solutions are represented by orthogonal series using the harmonic Steklov eigenfunctions. Error bounds for partial sums involving the lowest eigenfunctions are found. When the region is a rectangle, explicit formulae for the Steklov eigenfunctions and eigenvalues are known. These were used to find approximations for problems with known explicit solutions. Results about the accuracy of these solutions, as a function of the number of eigenfunctions used, are given. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free