Laplace eigenvalues and eigenvectors bounds

eigs_conf_str

First eigenvalue and eigenvector bounds on a square (structured mesh)

eigs_conf_unstr

First eigenvalue and eigenvector bounds on a square (unstructured mesh)

eigs_hole_mesh

Adaptively refined mesh

eigs_hole_incl

Inclusion for the first eigenvalue, domain with a hole

Main results:

  • guaranteed upper and lower bounds for an arbitrary simple eigenvalue;
  • guaranteed energy error bounds on the associated eigenvector;
  • efficiency (optimal convergenxce rate) and polynomial-degree robustness;
  • multiplicative constant tending to one under an elliptic regularity assumption on the corresponding
    source problem;
  • inexact algebraic solvers taken into account;
  • unified framework covering basically any numerical method (conforming, nonconforming, discontinuous Galerkin, and mixed finite elements).

Details: paper and preprint with Eric Cancès, Geneviève Dusson, Yvon Maday, and Benjamin Stamm, presentation

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