Journal article
Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations
- Abstract:
- We develop a discrete counterpart of the De Giorgi–Nash–Moser theory, which provides uniform Hölder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form −∇⋅(A∇u)=f−∇⋅F with A∈L∞(Ω;Rn×n) a uniformly elliptic matrix-valued function, f∈Lq(Ω), F∈Lp(Ω;Rn), 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 Ω⊂Rn.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 542.7KB, Terms of use)
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- Publisher copy:
- 10.1093/imanum/drab029
Authors
- Publisher:
- Oxford University Press
- Journal:
- IMA Journal of Numerical Analysis More from this journal
- Volume:
- 41
- Issue:
- 3
- Pages:
- 1846–1898
- Publication date:
- 2021-05-12
- Acceptance date:
- 2021-03-24
- DOI:
- EISSN:
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1464-3642
- ISSN:
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0272-4979
- Language:
-
English
- Keywords:
- Pubs id:
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1101288
- Local pid:
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pubs:1101288
- Deposit date:
-
2020-05-15
Terms of use
- Copyright holder:
- Diening et al.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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