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

Diening L, Scharle T, Süli E (2020)
IMA Journal of Numerical Analysis 41(3): 1846-1898.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Diening, LarsUniBi ; Scharle, Toni; Süli, Endre
Abstract / Bemerkung
We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Holder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form -del center dot (A del u) = f - del center dot F with A epsilon L-infinity (Omega; R-nxn) a uniformly elliptic matrix-valued function, f epsilon L-q(Omega), F epsilon L-p(Omega; 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 of R-n.
Erscheinungsjahr
2020
Zeitschriftentitel
IMA Journal of Numerical Analysis
Band
41
Ausgabe
3
Seite(n)
1846-1898
ISSN
0272-4979
eISSN
1464-3642
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. IMA Journal of Numerical Analysis . 2020;41(3):1846-1898.
Diening, L., Scharle, T., & Süli, E. (2020). Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. IMA Journal of Numerical Analysis , 41(3), 1846-1898. https://doi.org/10.1093/imanum/drab029
Diening, L., Scharle, T., and Süli, E. (2020). Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. IMA Journal of Numerical Analysis 41, 1846-1898.
Diening, L., Scharle, T., & Süli, E., 2020. Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. IMA Journal of Numerical Analysis , 41(3), p 1846-1898.
L. Diening, T. Scharle, and E. Süli, “Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations”, IMA Journal of Numerical Analysis , vol. 41, 2020, pp. 1846-1898.
Diening, L., Scharle, T., Süli, E.: Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations. IMA Journal of Numerical Analysis . 41, 1846-1898 (2020).
Diening, Lars, Scharle, Toni, and Süli, Endre. “Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations”. IMA Journal of Numerical Analysis 41.3 (2020): 1846-1898.

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arXiv: 2004.09341

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