### Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations

Diening L, Scharle T, Süli E (2020)
arXiv:2004.09341.

Preprint | Englisch

Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Diening, LarsUniBi ; Scharle, Toni; Süli, Endre
Einrichtung
Abstract / Bemerkung
We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform H\"older-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form $-\nabla \cdot(A\nabla u)=f-\nabla\cdot F$ with $A\in L^\infty(\Omega;\mathbb{R}^{n\times n})$ a uniformly elliptic matrix-valued function, $f\in L^{q}(\Omega)$, $F\in L^p(\Omega;\mathbb{R}^n)$, with $p > n$ and $q > n/2$, on $A$-nonobtuse shape-regular triangulations, which are not required to be quasi-uniform, of a bounded polyhedral Lipschitz domain $\Omega \subset \mathbb{R}^n$.
Erscheinungsjahr
2020
Zeitschriftentitel
arXiv:2004.09341
Page URI
https://pub.uni-bielefeld.de/record/2948394

### Zitieren

Diening L, Scharle T, Süli E. Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. arXiv:2004.09341. 2020.
Diening, L., Scharle, T., & Süli, E. (2020). Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. arXiv:2004.09341
Diening, L., Scharle, T., and Süli, E. (2020). Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. arXiv:2004.09341.
Diening, L., Scharle, T., & Süli, E., 2020. Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. arXiv:2004.09341.
L. Diening, T. Scharle, and E. Süli, “Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations”, arXiv:2004.09341, 2020.
Diening, L., Scharle, T., Süli, E.: Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. arXiv:2004.09341. (2020).
Diening, Lars, Scharle, Toni, and Süli, Endre. “Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations”. arXiv:2004.09341 (2020).

Open Data PUB

### Quellen

arXiv: 2004.09341