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

• Main Authors: López-Yela, A, Pérez-Pardo, J. M
• Format: Journal Article
• Language: English
• Published: 28-06-2017
• Subjects: Mathematics - Mathematical Physics; Mathematics - Numerical Analysis; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1606.02329

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.