Conference abstracts

Session B6 - Multiresolution and Adaptivity in Numerical PDEs

July 13, 18:30 ~ 18:55 - Room T1

$H^1$-stability of the $L^2$-projection and applications to adaptive methods

Fernando Gaspoz

University of Stuttgart, Germany   -   fernando.gaspoz@ians.uni-stuttgart.de

The $L^2$-projection onto discrete spaces plays an essential role in the analysis of finite element discretizations. On uniform grids $H^1$-stability of the $L^2$-projection can easily be deduced by an inverse estimate. This simple proof hinges on the fact that the minimal mesh-size is comparable to the maximal mesh-size. We provide a technique that sidestep this restriction and prove the stability in $H^1$ of the $L^2$-projection for piecewise continuous Finite Element Spaces for a class of adaptive meshes. We also present some new applications of this estimate.

Joint work with Claus-Justus Heine (University of Stuttgart, Germany) and Kunibert Siebert (University of Stuttgart, Germany).

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