A weak discrete maximum principle for hp-FEM
In this paper, we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM are available to the present day. Due to a negative result by H...
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| Format: | Journal article |
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2007
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| _version_ | 1797055411570868224 |
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| author | Šolín, P Vejchodský, T |
| author_facet | Šolín, P Vejchodský, T |
| author_sort | Šolín, P |
| collection | OXFORD |
| description | In this paper, we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM are available to the present day. Due to a negative result by Höhn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible. © 2006 Elsevier B.V. All rights reserved. |
| first_indexed | 2024-03-06T19:10:20Z |
| format | Journal article |
| id | oxford-uuid:169029cd-6cb8-43ca-af18-4e72f15679f9 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:10:20Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:169029cd-6cb8-43ca-af18-4e72f15679f92022-03-26T10:31:57ZA weak discrete maximum principle for hp-FEMJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:169029cd-6cb8-43ca-af18-4e72f15679f9Symplectic Elements at Oxford2007Šolín, PVejchodský, TIn this paper, we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM are available to the present day. Due to a negative result by Höhn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible. © 2006 Elsevier B.V. All rights reserved. |
| spellingShingle | Šolín, P Vejchodský, T A weak discrete maximum principle for hp-FEM |
| title | A weak discrete maximum principle for hp-FEM |
| title_full | A weak discrete maximum principle for hp-FEM |
| title_fullStr | A weak discrete maximum principle for hp-FEM |
| title_full_unstemmed | A weak discrete maximum principle for hp-FEM |
| title_short | A weak discrete maximum principle for hp-FEM |
| title_sort | weak discrete maximum principle for hp fem |
| work_keys_str_mv | AT solinp aweakdiscretemaximumprincipleforhpfem AT vejchodskyt aweakdiscretemaximumprincipleforhpfem AT solinp weakdiscretemaximumprincipleforhpfem AT vejchodskyt weakdiscretemaximumprincipleforhpfem |