P000018
Skeletal methods for direct guaranteed lower eigenvalue bounds
*Benedikt Gräßle (Humboldt-Universität zu Berlin)
Carsten Carstensen (Humboldt-Universität zu Berlin)
Tran Ngoc Tien (Universität Jena)
Conforming schemes directly compute guaranteed upper bounds on the exact eigenvalues by the min-max principle and the
rigorous estimation requires
access to guaranteed lower eigenvalue bounds (GLB).
This talk discusses the verifiable assumptions on the maximal mesh-size and discretisation parameters that result in
direct GLB for the hybrid-high order (HHO) eigenvalue solver of Carstensen-Ern-Puttkammer [Numer.Math. 149, 2021] and its recent modification with an even simpler p-robust parameter selection.
Both schemes come with an a priori quasi-best approximation property and allow a stabilization-free reliable and efficient a posteriori error control.
Computer benchmarks provide striking numerical evidence for optimal high-order convergence rates of the associated adaptive mesh-refining algorithm.