Publication: Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary
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2017-10-15
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Elsevier
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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.
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Self-adjoint extensions, Spectral problem, Laplace, Higher dimension, Boundary conditions, Finite element method
Bibliographic citation
López-Yela, A., Pérez-Pardo, J. M. (2017). Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace–Beltrami operator on manifolds with a boundary. Journal of Computational Physics, 347, 235–260.