STEFANO GIANI
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Convergence for Eigenvalue Problems with Mesh Adaptivity

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), 1067-1091.

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 NI07054-HOP, (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)

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