An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization Article Swipe
Marcel Braukhoff
,
Ilaria Perugia
,
Paul Stocker
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1137/20m1360086
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1137/20m1360086
Cross-diffusion systems are systems of nonlinear parabolic partial\ndifferential equations that are used to describe dynamical processes in several\napplication, including chemical concentrations and cell biology. We present a\nspace-time approach to the proof of existence of bounded weak solutions of\ncross-diffusion systems, making use of the system entropy to examine long-term\nbehavior and to show that the solution is nonnegative, even when a maximum\nprinciple is not available. This approach naturally gives rise to a novel\nspace-time Galerkin method for the numerical approximation of cross-diffusion\nsystems that conserves their entropy structure. We prove existence and\nconvergence of the discrete solutions, and present numerical results for the\nporous medium, the Fisher-KPP, and the Maxwell-Stefan problem.\n
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1137/20m1360086
- OA Status
- green
- Cited By
- 8
- References
- 52
- Related Works
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- OpenAlex ID
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https://openalex.org/W4213113120Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1137/20m1360086Digital Object Identifier
- Title
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An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin DiscretizationWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-02-01Full publication date if available
- Authors
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Marcel Braukhoff, Ilaria Perugia, Paul StockerList of authors in order
- Landing page
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https://doi.org/10.1137/20m1360086Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2006.13069Direct OA link when available
- Concepts
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Mathematics, Discretization, Galerkin method, Discontinuous Galerkin method, Applied mathematics, Mathematical analysis, Entropy (arrow of time), Space time, Finite element method, Thermodynamics, Chemical engineering, Quantum mechanics, Engineering, PhysicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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8Total citation count in OpenAlex
- Citations by year (recent)
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2024: 3, 2023: 4, 2022: 1Per-year citation counts (last 5 years)
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52Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.novel\nspace-time | 70 |
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| countries_distinct_count | 2 |
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| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |