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Article
Benchmark Results for Testing Adaptive Finite Element Eigenvalue Procedures II (Cluster Robust Eigenvector and Eigenvalue Estimates)
Mathematics and Statistics Faculty Publications and Presentations
  • Stefano Giani, Durham University
  • Luka Grubisic
  • Jeffrey S. Ovall, Portland State University
Document Type
Pre-Print
Publication Date
1-1-2012
Subjects
  • Partial differential equations -- Numerical solutions,
  • Eigenvalues -- Estimation,
  • Eigenvectors
Abstract
As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.
Description

This is the pre-print of an article which was subsequently published in Applied Numerical Mathematics, Copyright (2012) Elsevier

Persistent Identifier
http://archives.pdx.edu/ds/psu/16187
Citation Information
Stefano Giani, Luka Grubisic and Jeffrey S. Ovall. "Benchmark Results for Testing Adaptive Finite Element Eigenvalue Procedures II (Cluster Robust Eigenvector and Eigenvalue Estimates)" (2012)
Available at: http://works.bepress.com/jeffrey_ovall/5/