Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations
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 functi...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Oxford University Press
2021
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| _version_ | 1797067335436075008 |
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| author | Diening, L Scharle, T Süli, E |
| author_facet | Diening, L Scharle, T Süli, E |
| author_sort | Diening, L |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T21:54:48Z |
| format | Journal article |
| id | oxford-uuid:4c8b4e15-f507-4829-b1d2-89f94d7f022b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:54:48Z |
| publishDate | 2021 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:4c8b4e15-f507-4829-b1d2-89f94d7f022b2022-03-26T15:50:07ZUniform Hölder-norm bounds for finite element approximations of second-order elliptic equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4c8b4e15-f507-4829-b1d2-89f94d7f022bEnglishSymplectic ElementsOxford University Press2021Diening, LScharle, TSüli, EWe 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. |
| spellingShingle | Diening, L Scharle, T Süli, E Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations |
| title | Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations |
| title_full | Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations |
| title_fullStr | Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations |
| title_full_unstemmed | Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations |
| title_short | Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations |
| title_sort | uniform holder norm bounds for finite element approximations of second order elliptic equations |
| work_keys_str_mv | AT dieningl uniformholdernormboundsforfiniteelementapproximationsofsecondorderellipticequations AT scharlet uniformholdernormboundsforfiniteelementapproximationsofsecondorderellipticequations AT sulie uniformholdernormboundsforfiniteelementapproximationsofsecondorderellipticequations |