Positivity preserving finite element approximation

Authors:
Ricardo H. Nochetto and Lars B. Wahlbin

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

Published electronically:
November 20, 2001

MathSciNet review:
1933037

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Abstract: We consider finite element operators defined on ``rough'' functions in a bounded polyhedron in . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of 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 . 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.

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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

Email:
rhn@math.umd.edu

**Lars B. Wahlbin**

Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853

Email:
wahlbin@math.cornell.edu

DOI:
https://doi.org/10.1090/S0025-5718-01-01369-2

Keywords:
Positive operators,
finite elements,
extreme points,
second order accuracy

Received by editor(s):
November 5, 1999

Received by editor(s) in revised form:
November 21, 2000

Published electronically:
November 20, 2001

Article copyright:
© Copyright 2001
American Mathematical Society