Sparsity comparison of polytopal finite element methods Article Swipe
Christoph Lehrenfeld
,
Paul Stocker
,
Maximilian Zienecker
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1002/pamm.202400150
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1002/pamm.202400150
In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations on polytopal meshes. We consider the virtual element method (VEM) and different discontinuous Galerkin (DG) methods, namely, the Hybrid DG and Trefftz DG methods. The VEM is a conforming method, that can be seen as a generalization of the classic finite element method to arbitrary polytopal meshes. DG methods are non‐conforming methods that offer high flexibility, but also come with high computational costs. Hybridization reduces these costs by introducing additional facet variables, onto which the computational costs can be transferred to. Trefftz DG methods achieve a similar reduction in complexity by selecting a special and smaller set of basis functions on each element. The association of computational costs to different geometrical entities (elements or facets) leads to differences in the performance of these methods on different grid types. This paper aims to compare the dependency of these approaches across different grid configurations.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1002/pamm.202400150
- OA Status
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- Cited By
- 3
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- 21
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https://openalex.org/W4403135799Canonical identifier for this work in OpenAlex
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https://doi.org/10.1002/pamm.202400150Digital Object Identifier
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Sparsity comparison of polytopal finite element methodsWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-10-01Full publication date if available
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Christoph Lehrenfeld, Paul Stocker, Maximilian ZieneckerList of authors in order
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https://doi.org/10.1002/pamm.202400150Publisher landing page
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1002/pamm.202400150Direct OA link when available
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Finite element method, Mathematics, Computer science, Applied mathematics, Structural engineering, EngineeringTop concepts (fields/topics) attached by OpenAlex
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3Total citation count in OpenAlex
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2025: 1, 2024: 2Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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