# A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace-Beltrami Operator

@article{Bonito2018APE, title={A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace-Beltrami Operator}, author={Andrea Bonito and Alan Demlow and Justin Owen}, journal={SIAM J. Numer. Anal.}, year={2018}, volume={56}, pages={2963-2988} }

Elliptic partial differential equations on surfaces play an essential role in geometry, relativity theory, phase transitions, materials science, image processing, and other applications. They are typically governed by the Laplace-Beltrami operator. We present and analyze approximations by Surface Finite Element Methods (SFEM) of the Laplace-Beltrami eigenvalue problem. As for SFEM for source problems, spectral approximation is challenged by two sources of errors: the geometric consistency error…

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