On the nodal set of the eigenfunctions of the Laplace-Beltrami operator for bounded surfaces in \(\mathbb R^3\): a computational approach

DOI10.3934/cpaa.2014.13.2115zbMath1304.65244OpenAlexW2322289266MaRDI QIDQ479343

Roland Glowinski, Andrea Bonito

Publication date: 5 December 2014

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2014.13.2115

zbMATH Keywords

finite element methodseigenfunctionsLaplace-Beltrami operatorsurfaceseigenpaireigenvalue/eigenfunction problemNodal linesring torus

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Elliptic equations on manifolds, general theory (58J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Uses Software

• SLEPc
• deal.ii
• ARPACK

Cites Work

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• ARPACK Users' Guide
• On the numerical solution of a semilinear elliptic eigenproblem of Lane–Emden type, II: Numerical experiments