Resolving Boundary Layers with Harmonic Extension Finite Elements
In recent years, the standard numerical methods for partial differential equations have been extended with variants that address the issue of domain discretisation in complicated domains. Sometimes similar requirements are induced by local parameter-dependent features of the solutions, for instance,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/27/4/57 |
| _version_ | 1827599177194930176 |
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| author | Harri Hakula |
| author_facet | Harri Hakula |
| author_sort | Harri Hakula |
| collection | DOAJ |
| description | In recent years, the standard numerical methods for partial differential equations have been extended with variants that address the issue of domain discretisation in complicated domains. Sometimes similar requirements are induced by local parameter-dependent features of the solutions, for instance, boundary or internal layers. The adaptive reference elements are one way with which harmonic extension elements, an extension of the <i>p</i>-version of the finite element method, can be implemented. In combination with simple replacement rule-based mesh generation, the performance of the method is shown to be equivalent to that of the standard <i>p</i>-version in problems where the boundary layers dominate the solution. The performance over a parameter range is demonstrated in an application of computational asymptotic analysis, where known estimates are recovered via computational means only. |
| first_indexed | 2024-03-09T04:07:57Z |
| format | Article |
| id | doaj.art-a45504758525447685ff8c6f800f9caa |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T04:07:57Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-a45504758525447685ff8c6f800f9caa2023-12-03T14:04:03ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472022-07-012745710.3390/mca27040057Resolving Boundary Layers with Harmonic Extension Finite ElementsHarri Hakula0Department of Mathematics and Systems Analysis, Aalto University, Otakaari 1, FI-00076 Aalto, FinlandIn recent years, the standard numerical methods for partial differential equations have been extended with variants that address the issue of domain discretisation in complicated domains. Sometimes similar requirements are induced by local parameter-dependent features of the solutions, for instance, boundary or internal layers. The adaptive reference elements are one way with which harmonic extension elements, an extension of the <i>p</i>-version of the finite element method, can be implemented. In combination with simple replacement rule-based mesh generation, the performance of the method is shown to be equivalent to that of the standard <i>p</i>-version in problems where the boundary layers dominate the solution. The performance over a parameter range is demonstrated in an application of computational asymptotic analysis, where known estimates are recovered via computational means only.https://www.mdpi.com/2297-8747/27/4/57finite element methodp-versionharmonic extensions |
| spellingShingle | Harri Hakula Resolving Boundary Layers with Harmonic Extension Finite Elements Mathematical and Computational Applications finite element method p-version harmonic extensions |
| title | Resolving Boundary Layers with Harmonic Extension Finite Elements |
| title_full | Resolving Boundary Layers with Harmonic Extension Finite Elements |
| title_fullStr | Resolving Boundary Layers with Harmonic Extension Finite Elements |
| title_full_unstemmed | Resolving Boundary Layers with Harmonic Extension Finite Elements |
| title_short | Resolving Boundary Layers with Harmonic Extension Finite Elements |
| title_sort | resolving boundary layers with harmonic extension finite elements |
| topic | finite element method p-version harmonic extensions |
| url | https://www.mdpi.com/2297-8747/27/4/57 |
| work_keys_str_mv | AT harrihakula resolvingboundarylayerswithharmonicextensionfiniteelements |