Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues

0489966 - MÚ 2019 RIV NL eng J - Journal Article
Vejchodský, Tomáš
Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues.
Journal of Computational and Applied Mathematics. Roč. 340, October 1 (2018), s. 676-690. ISSN 0377-0427. E-ISSN 1879-1778
Institutional support: RVO:67985840
Keywords : eigenproblem * guaranteed * finite element method
OECD category: Pure mathematics
Impact factor: 1.883, year: 2018
https://www.sciencedirect.com/science/article/pii/S0377042718301134

The standard application of the Lehmann-Goerisch method for lower bounds on eigenvalues of symmetric elliptic second-order partial differential operators relies on determination of fluxes. These fluxes are usually computed by solving a global saddle point problem. In this paper we propose a simpler global problem that yields these fluxes of the same quality. The simplified problem is smaller, it is positive definite, and any H(div) conforming finite elements, such as Raviart-Thomas elements, can be used for its solution. In addition, these global problems can be split into a number of independent local problems on patches, which allows for trivial parallelization. The computational performance of these approaches is illustrated by numerical examples for Laplace and Steklov type eigenvalue problems. These examples also show that local flux reconstructions enable computation of lower bounds on eigenvalues on considerably finer meshes than the traditional global reconstructions.
Permanent Link: http://hdl.handle.net/11104/0284261