Thursday, November 16, 2023 - 14:30 in V2-210/216
Pointwise gradient estimate of the Ritz projection
A talk in the BI.discrete Workshop series by
Julian Rolfes from Bielefeld
| Abstract: |
Let $\Omega \subset \mathbb{R}^n$ be a convex polytope ($n \leq 3$). The Ritz projection is the best approximation, in the $W^{1,2}_0$-norm, to a given function in a finite element space. When such finite element spaces are constructed on the basis of quasiuniform triangulations, we show a pointwise estimate on the Ritz projection. Namely, that the gradient at any point in $\Omega$ is controlled by the Hardy--Littlewood maximal function of the gradient of the original function at the same point. From this estimate, the stability of the Ritz projection on a wide range of spaces that are of interest in the analysis of PDEs immediately follows. Among those are weighted spaces, Orlicz spaces and Lorentz spaces.
This is joint work with Lars Diening and Abner J. Salgado.
Within the CRC this talk is associated to the project(s): A7, B3, B7 |
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