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Article
Reliable A-Posteriori Error Estimators for hp-Adaptive Finite Element Approximations of Eigenvalue/lEigenvector Problems
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
12-1-2011
Subjects
  • Partial differential equations -- Numerical solutions,
  • Eigenvalues -- Estimation,
  • Eigenvectors,
  • Boundary value problems
Abstract
We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.
Description

Pre-print of an article submitted for consideration. Copyright (2011) Giani, Grubisic, Ovall.

Persistent Identifier
http://archives.pdx.edu/ds/psu/16194
Citation Information
Giani, S., Grubišić, L., & Ovall, J. (2011). Reliable a-posteriori error estimators for $ hp $-adaptive finite element approximations of eigenvalue/eigenvector problems. arXiv preprint arXiv:1112.0436.