Hermite interpolation of nonsmooth functions preserving boundary conditions

Girault, V.; Scott, L.

doi:10.1090/S0025-5718-02-01446-1

Hermite interpolation of nonsmooth functions preserving boundary conditions
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by V. Girault and L. R. Scott;

Math. Comp. 71 (2002), 1043-1074

DOI: https://doi.org/10.1090/S0025-5718-02-01446-1

Published electronically: January 17, 2002

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Abstract:

This article is devoted to the construction of a Hermite-type regularization operator transforming functions that are not necessarily ${\mathcal C}^1$ into globally ${\mathcal C}^1$ finite-element functions that are piecewise polynomials. This regularization operator is a projection, it preserves appropriate first and second order polynomial traces, and it has approximation properties of optimal order. As an illustration, it is used to discretize a nonhomogeneous Navier-Stokes problem, with tangential boundary condition.

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