This
project has been done in collaboration with Prof. Ivan
Graham.
Summary:
We
prove the convergence of an adaptive linear finite element
method for computing eigenvalues and eigenfunctions of second order
symmetric elliptic partial differential operators. Each step of the
adaptive procedure refines elements according to a properly designed
marking strategy. The error analysis extends the standard theory of
convergence of adaptive methods for linear elliptic source problems to
the elliptic eigenvalue problem, and in particular deals with various
complications which arise essentially from the nonlinearity of the
eigenvalue problem.
The material in these pages is not a comprehensive analysis
of our method. For more information refer to:
S.
Giani and
I.G. Graham, A convergent adaptive method for
elliptic eigenvalue
problems.
 Bath
Institute for Complex Systems Preprint number 13/07
,
University of Bath (2007)
Sections:
Definition of the problem
A posteriori analysis
Convergence result
Numerics
Bibliography
References:
S. Giani and I.G. Graham (2009), A convergent adaptive method for elliptic eigenvalue problems
 SIAM J. Numer. Anal. 47(2), 10671091.
S. Giani and I.G. Graham,
A convergent adaptive method for elliptic eigenvalue problems and numerical experiments.  Bath Institute for Complex Systems Preprint number 14/08, (2008)
S. Giani and I.G. Graham,
A convergent adaptive method for elliptic eigenvalue.  Isaac Newton Institute for Mathematical Sciences Preprints NI07054HOP, (2007)
S. Giani and I.G. Graham,
A convergent adaptive method for elliptic eigenvalue problems.  Bath Institute for Complex Systems Preprint number 6/07, (2007)
