arXiv subjects

Gabriel Raúl Barrenechea

Publications and source records attributed to Gabriel Raúl Barrenechea.

3 recordsLinked to original sources

arXiv2014

Eigenvalue enclosures

This paper is concerned with methods for numerical computation of eigenvalue enclosures. We examine in close detail the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a geometrically motivated method developed more recently by Davies and Plum. We extend various previously known results in the theory and establish explicit convergence estimates in both settings. The theoretical results are supported by two benchmark numerical experiments on the isotropic Maxwell eigenvalue problem.

math.NA↗

arXiv2014

Finite element eigenvalue enclosures for the Maxwell operator

We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange elements and unstructured meshes.

math.AP↗

arXiv2011

A local projection stabilized method for fictitious domains

In this work a local projection stabilization method is proposed to solve a fictitious domain problem. The method adds a suitable fluctuation term to the formulation thus rendering the natural space for the Lagrange multiplier stable. Stability and convergence are proved and these results are illustrated by a numerical experiment.

math.NA↗