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Convergence for Eigenvalue Problems with Mesh Adaptivity

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Bibliography:

1 M. Ainsworth and J.T. Oden, A Posterior Error Estimation in Finite Element Analysis, Wiley, 2000.
 
2 I. Babuška,
The finite element method for elliptic equations with discontinuous coefficients
Computing 5: 207-213, 1970.
 
3 I. Babuška and J. Osborn.
Eigenvalue Problems, in Handbook of Numerical Analysis Vol II, eds P.G. Cairlet and J.L. Lions, North Holland, 641-787, 1991.
 
4 M. Bourland, M. Dauge, M.-S. Lubuma and S. Nicaise,
Coefficients of the singularities for elliptic boundary value problems on domains with conical points. III: Finite element methods on polygonal domains,
SIAM J. Numer. Anal. 29: 136-155, 1992.
 
5 R.G. Durán, C. Padra and R. Rodríguez,
A posteriori estimates for the finite element approximation of eigenvalue problems,
Math. Mod. Meth. Appl. Sci. 13(8), 1219-1229, 2003.
 
6 S. C. Brenner and L. R. Scott.
The Mathematical Theory of Finite Element Methods.
Springer-Verlag, Berlin, 2002.
 
7 C. Carstensen and R. H. W. Hoppe.
Convergence analysis of an adaptive nonconforming finite element method.
Numer. Math., (103):251-266, 2006.
 
8 C. Carstensen and R. H. W. Hoppe.
Error reduction and convergence for an adaptive mixed finite element method.
Math. Comp., 75(255):1033-1042, 2006.
 
9 P. G. Ciarlet.
The Finite Element Method for Elliptic Problems.
SIAM, Philadelphia, 2002.
 
10 W. Dorfler.
A convergent adaptive algorithm for Poisson's equation.
SIAM J. Numer. Anal., 33:1106-1124, 1996.
 
11 S. Giani.
Convergence adaptive finite element methods for elliptic eigenvalue problems with application to photonic crystal fibers (PCFs),
PhD Thesis, University of Bath, 2007.
 
12 W. Hackbusch.
Elliptic Differential Equations.
Springer, 1992.
 
13 M.G. Larson,
A posteriori and a priori analysis for finite element approximations of self-adjoint elliptic eigenvalue problems
SIAM J. Numer. Anal. 38:608-625, 2000.
 
14 R. B. Lehoucq, D. C. Sorensen, and C. Yang,
ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods,
SIAM, 1998.
 
15 K. Mekchay and R. H. Nochetto.
Convergence of adaptive finite element methods for general second order linear elliptic pdes.
SIAM J. Numer. Anal., 43:1803-1827, 2005.
 
16 P. Morin, R. H. Nochetto and K. G. Siebert.
Data oscillation and convergence of adaptive fem.
SIAM J. Numer. Anal., 38:466-488, 2000.
 
17 J. A. Scott,
Sparse Direct Methods: An Introduction.
Lecture Notes in Physics, 535, 401, 2000.
 
18 HSL archive, http://hsl.rl.ac.uk/archive/hslarchive.html
 
19 R. L. Scott, S. Zhang,
Finite element interpolation of nonsmooth functions satisfying boundary conditions,
Math Comp, 54:483-493,1990.
 
20 A. Schmidt, K. G. Siebert,
ALBERTA: An adaptive hierarchical finite element toolbox,
Manual, 244 p., Preprint 06/2000 Freiburg.
 
21 G. Strang and G. J. Fix.
An Analysis of the Finite Element Method.
Prentice-Hall, 1973.
 
22 T.F. Walsh, G.M. Reese and U.L. Hetmaniuk,
Explicit a posteriori error estimates for eigenvalue analysis of heterogeneous elastic structures, Technical Report 4237, Sandia National Laboratories, 2005.

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