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**Positivity preserving finite element approximation.**
*(English)*
Zbl 1001.41011

In this paper, finite elements on quasi-uniform partitions into simplices are studied. In two dimensions, the partitions are the usual triangulations, but the results in this paper work in higher dimensions, where general simplices are used, as well. The particular question addressed is whether there are higher order accurate approximations by finite elements on such partitions if positivity preservation is required. The approximation is by a Lagrange finite element reproducing a finite element operator which is positive and bounded. There is an impossibility result on the approximation of general functions to higher order accuracy at extreme points of a domain.

Reviewer: Martin Buhmann (Giessen)

### MSC:

41A25 | Rate of convergence, degree of approximation |

41A36 | Approximation by positive operators |

65D05 | Numerical interpolation |

65N15 | Error bounds for boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

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\textit{R. H. Nochetto} and \textit{L. B. Wahlbin}, Math. Comput. 71, No. 240, 1405--1419 (2002; Zbl 1001.41011)

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### References:

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