Optimal convergence for the finite element method in Campanato spaces
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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 $W^{1,p}$âestimates and give a new proof of the well-known $W^{1,\infty }$âresults of Rannacher and Scott.References
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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
- 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 âLa Sapienzaâ.
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1677478