Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary Articles uri icon

publication date

  • October 2017

start page

  • 235

end page

  • 260

volume

  • 347

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

abstract

  • A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large class of self-adjoint extensions of Laplace-Beltrami operators in terms of their associated quadratic forms. The convergence of the scheme is proved. A two-dimensional version of the algorithm is implemented effectively and several numerical examples are computed showing that the algorithm treats in a unified way a wide variety of boundary conditions.

keywords

  • self-adjoint extensions; spectral problem; laplace; higher dimension; boundary conditions; finite element method