Poincaré-Friedrichs type constants for operators involving grad, curl, and div: Theory and numerical experiments

0522489 - ÚTIA 2021 RIV GB eng J - Journal Article
Pauly, D. - Valdman, Jan
Poincaré-Friedrichs type constants for operators involving grad, curl, and div: Theory and numerical experiments.
Computers & Mathematics With Applications. Roč. 79, č. 11 (2020), s. 3027-3067. ISSN 0898-1221. E-ISSN 1873-7668
R&D Projects: GA ČR(CZ) GF19-29646L
Institutional support: RVO:67985556
Keywords : Friedrichs constants * Poincaré constants * Maxwell constants * Dirichlet eigenvalues * Neumann eigenvalues * Maxwell eigenvalues
OECD category: Applied mathematics
Impact factor: 3.476, year: 2020
Method of publishing: Limited access
https://www.sciencedirect.com/science/article/pii/S0898122120300110 http://library.utia.cas.cz/separaty/2020/MTR/valdman-0522489.pdf

We give some theoretical as well as computational results on Laplace and Maxwell constants. Besides the classical de Rham complex we investigate the complex of elasticity and the complex related to the biharmonic equation and general relativity as well using the general function alanalytical concept of Hilbert complexes. We consider mixed boundary conditions and bounded Lipschitz domains of arbitrary topology. Our numerical aspects are presented by examples for the de Rham complex in 2D and 3D which not only confirm our theoretical findings but also indicate some interesting conjectures.
Permanent Link: http://hdl.handle.net/11104/0306967