Generalized weak Galerkin finite element methods for second order elliptic problems Article Swipe
Dan Li
,
Chunmei Wang
,
Junping Wang
,
Xiu Ye
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2305.08736
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2305.08736
This article proposes and analyzes the generalized weak Galerkin ({\rm g}WG) finite element method for the second order elliptic problem. A generalized discrete weak gradient operator is introduced in the weak Galerkin framework so that the {\rm g}WG methods would not only allow arbitrary combinations of piecewise polynomials defined in the interior and on the boundary of each local finite element, but also work on general polytopal partitions. Error estimates are established for the corresponding numerical functions in the energy norm and the usual $L^2$ norm. A series of numerical experiments are presented to demonstrate the performance of the newly proposed {\rm g}WG method.
Related Topics
Concepts
Mathematics
Finite element method
Norm (philosophy)
Galerkin method
Piecewise
Discontinuous Galerkin method
Mathematical analysis
Order (exchange)
Numerical analysis
Boundary value problem
Operator (biology)
Applied mathematics
Physics
Thermodynamics
Repressor
Chemistry
Economics
Law
Biochemistry
Political science
Gene
Finance
Transcription factor
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2305.08736
- https://arxiv.org/pdf/2305.08736
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4376876122
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4376876122Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2305.08736Digital Object Identifier
- Title
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Generalized weak Galerkin finite element methods for second order elliptic problemsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2023Year of publication
- Publication date
-
2023-05-15Full publication date if available
- Authors
-
Dan Li, Chunmei Wang, Junping Wang, Xiu YeList of authors in order
- Landing page
-
https://arxiv.org/abs/2305.08736Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2305.08736Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2305.08736Direct OA link when available
- Concepts
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Mathematics, Finite element method, Norm (philosophy), Galerkin method, Piecewise, Discontinuous Galerkin method, Mathematical analysis, Order (exchange), Numerical analysis, Boundary value problem, Operator (biology), Applied mathematics, Physics, Thermodynamics, Repressor, Chemistry, Economics, Law, Biochemistry, Political science, Gene, Finance, Transcription factorTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2024: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.polytopal | 66 |
| abstract_inverted_index.presented | 92 |
| abstract_inverted_index.introduced | 27 |
| abstract_inverted_index.demonstrate | 94 |
| abstract_inverted_index.established | 71 |
| abstract_inverted_index.experiments | 90 |
| abstract_inverted_index.generalized | 6, 21 |
| abstract_inverted_index.partitions. | 67 |
| abstract_inverted_index.performance | 96 |
| abstract_inverted_index.polynomials | 47 |
| abstract_inverted_index.combinations | 44 |
| abstract_inverted_index.corresponding | 74 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.7099999785423279 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile |