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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Optimal convergence
for the finite element method
in Campanato spaces


Author: Georg Dolzmann
Journal: Math. Comp. 68 (1999), 1397-1427
MSC (1991): Primary 65N12; Secondary 65N15, 65N30
DOI: https://doi.org/10.1090/S0025-5718-99-01175-8
Published electronically: May 25, 1999
MathSciNet review: 1677478
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Abstract: We prove a priori estimates and optimal error estimates for linear finite element approximations of elliptic systems in divergence form with continuous coefficients in Campanato spaces. The proofs rely on discrete analogues of the Campanato inequalities for the solution of the system, which locally measure the decay of the energy. As an application of our results we derive $W^{1,p}$-estimates and give a new proof of the well-known $W^{1,\infty}$-results of Rannacher and Scott.


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Additional Information

Georg Dolzmann
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany
Email: georg@mis.mpg.de

DOI: https://doi.org/10.1090/S0025-5718-99-01175-8
Keywords: Optimal error estimates, finite element methods, Campanato spaces
Received by editor(s): September 26, 1994
Received by editor(s) in revised form: October 2, 1997
Published electronically: May 25, 1999
Additional Notes: Partially supported by the Center for Nonlinear Analysis at Carnegie Mellon University, Pittsburgh and by Human Capital and Mobility, contract number ERBCHBGCT920004 at the University of Rome “La Sapienza”.
Article copyright: © Copyright 1999 American Mathematical Society