SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection–diffusion equation Article Swipe
L. Beirão da Veiga
,
Franco Dassi
,
Sergio Gómez
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1016/j.cma.2024.117722
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1016/j.cma.2024.117722
We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent advection–diffusion equation. A space–time streamline-upwind Petrov–Galerkin term is used to stabilize the method. More precisely, we show that the method is inf–sup stable with constant independent of the diffusion coefficient, which ensures the robustness of the method in the convection- and diffusion-dominated regimes. Moreover, we prove optimal convergence rates in both regimes for the error in the energy norm. An important feature of the presented analysis is the control in the full L2(0,T;L2(Ω)) norm without the need of introducing an artificial reaction term in the model. We finally present some numerical experiments in (3+1)-dimensions that validate our theoretical results.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.cma.2024.117722
- OA Status
- hybrid
- Cited By
- 2
- References
- 46
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4406366949Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1016/j.cma.2024.117722Digital Object Identifier
- Title
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SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection–diffusion equationWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-01-14Full publication date if available
- Authors
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L. Beirão da Veiga, Franco Dassi, Sergio GómezList of authors in order
- Landing page
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https://doi.org/10.1016/j.cma.2024.117722Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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hybridOpen access status per OpenAlex
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https://doi.org/10.1016/j.cma.2024.117722Direct OA link when available
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Advection, Finite element method, Diffusion, Convection–diffusion equation, Diffusion equation, Mechanics, Mathematics, Mathematical analysis, Applied mathematics, Physics, Computer science, Engineering, Thermodynamics, Metric (unit), Operations managementTop concepts (fields/topics) attached by OpenAlex
- Cited by
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2Total citation count in OpenAlex
- Citations by year (recent)
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2025: 2Per-year citation counts (last 5 years)
- References (count)
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46Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.finite | 17 |
| abstract_inverted_index.method | 51, 68 |
| abstract_inverted_index.model. | 117 |
| abstract_inverted_index.scheme | 12 |
| abstract_inverted_index.stable | 54 |
| abstract_inverted_index.applied | 28 |
| abstract_inverted_index.control | 100 |
| abstract_inverted_index.element | 20 |
| abstract_inverted_index.ensures | 63 |
| abstract_inverted_index.feature | 93 |
| abstract_inverted_index.finally | 119 |
| abstract_inverted_index.method. | 44 |
| abstract_inverted_index.optimal | 78 |
| abstract_inverted_index.present | 120 |
| abstract_inverted_index.regimes | 83 |
| abstract_inverted_index.spatial | 21 |
| abstract_inverted_index.virtual | 19 |
| abstract_inverted_index.without | 106 |
| abstract_inverted_index.Galerkin | 26 |
| abstract_inverted_index.analysis | 7, 97 |
| abstract_inverted_index.constant | 56 |
| abstract_inverted_index.discrete | 11 |
| abstract_inverted_index.obtained | 13 |
| abstract_inverted_index.reaction | 113 |
| abstract_inverted_index.regimes. | 74 |
| abstract_inverted_index.results. | 130 |
| abstract_inverted_index.validate | 127 |
| abstract_inverted_index.Moreover, | 75 |
| abstract_inverted_index.combining | 15 |
| abstract_inverted_index.diffusion | 60 |
| abstract_inverted_index.equation. | 33 |
| abstract_inverted_index.important | 92 |
| abstract_inverted_index.inf–sup | 53 |
| abstract_inverted_index.numerical | 122 |
| abstract_inverted_index.presented | 96 |
| abstract_inverted_index.stability | 4 |
| abstract_inverted_index.stabilize | 42 |
| abstract_inverted_index.artificial | 112 |
| abstract_inverted_index.precisely, | 46 |
| abstract_inverted_index.robustness | 65 |
| abstract_inverted_index.convection- | 71 |
| abstract_inverted_index.convergence | 6, 79 |
| abstract_inverted_index.experiments | 123 |
| abstract_inverted_index.independent | 57 |
| abstract_inverted_index.introducing | 110 |
| abstract_inverted_index.theoretical | 129 |
| abstract_inverted_index.coefficient, | 61 |
| abstract_inverted_index.space–time | 35 |
| abstract_inverted_index.time-stepping | 27 |
| abstract_inverted_index.L2(0,T;L2(Ω)) | 104 |
| abstract_inverted_index.discretization | 22 |
| abstract_inverted_index.time-dependent | 31 |
| abstract_inverted_index.(3+1)-dimensions | 125 |
| abstract_inverted_index.Petrov–Galerkin | 37 |
| abstract_inverted_index.streamline-upwind | 36 |
| abstract_inverted_index.diffusion-dominated | 73 |
| abstract_inverted_index.upwind-discontinuous | 25 |
| abstract_inverted_index.advection–diffusion | 32 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 95 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.91891892 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |