Positivity preserving finite element approximation
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- by Ricardo H. Nochetto and Lars B. Wahlbin PDF
- Math. Comp. 71 (2002), 1405-1419 Request permission
Abstract:
We consider finite element operators defined on “rough” functions in a bounded polyhedron $\Omega$ in $\mathbb {R}^N$. Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of $\Omega$ and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of $\Omega$. We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.References
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Additional Information
- Ricardo H. Nochetto
- Affiliation: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
- MR Author ID: 131850
- Email: rhn@math.umd.edu
- Lars B. Wahlbin
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- Email: wahlbin@math.cornell.edu
- Received by editor(s): November 5, 1999
- Received by editor(s) in revised form: November 21, 2000
- Published electronically: November 20, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 1405-1419
- MSC (2000): Primary 41A25, 41A36, 65D05, 65N15, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-01-01369-2
- MathSciNet review: 1933037