Poincare-Friedrichs Type Constants for Operators Involving grad, curl, and div: Theory and Numerical Experiments
Analysis of PDEs
2020-01-14 v4 Numerical Analysis
Functional Analysis
Numerical Analysis
Abstract
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 functional analytical 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.
Keywords
Cite
@article{arxiv.1909.11563,
title = {Poincare-Friedrichs Type Constants for Operators Involving grad, curl, and div: Theory and Numerical Experiments},
author = {Dirk Pauly and Jan Valdman},
journal= {arXiv preprint arXiv:1909.11563},
year = {2020}
}
Comments
42 pages, 10 figures