TY - JOUR
T1 - Local two-sided bounds for eigenvalues of self-adjoint operators
AU - Barrenechea, Gabriel
AU - Boulton, Lyonell
AU - Boussaid, Nabile
PY - 2016/6/18
Y1 - 2016/6/18
N2 - We examine 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 establish a general framework which allows sharpening various previously known results in these two settings and determine explicit convergence estimates for both methods. We demonstrate the applicability of the method of Zimmermann and Mertins by means of numerical tests on the resonant cavity problem.
AB - We examine 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 establish a general framework which allows sharpening various previously known results in these two settings and determine explicit convergence estimates for both methods. We demonstrate the applicability of the method of Zimmermann and Mertins by means of numerical tests on the resonant cavity problem.
KW - Eigenvalue enclosures
KW - spectral pollution
KW - finite element method
KW - Maxwell equation
UR - http://link.springer.com/journal/211
U2 - 10.1007/s00211-016-0822-1
DO - 10.1007/s00211-016-0822-1
M3 - Article
SN - 0029-599X
JO - Numerische Mathematik
JF - Numerische Mathematik
ER -
