Stable $C^1$-conforming finite element methods for a class of nonlinear fourth-order evolution equations Article Swipe
Agus L. Soenjaya
,
Thanh Tran
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2309.05530
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2309.05530
We propose some finite element schemes to solve a class of fourth-order nonlinear PDEs, which include the vector-valued Landau--Lifshitz--Baryakhtar equation, the Swift--Hohenberg equation, and various Cahn--Hilliard-type equations with source and convection terms, among others. The proposed numerical methods include a spatially semi-discrete scheme and two linearised fully-discrete $C^1$-conforming schemes utilising a semi-implicit Euler method and a semi-implicit BDF method. We show that these numerical schemes are stable in $\mathbb{H}^2$. Error analysis is performed which shows optimal convergence rates in each scheme. Numerical experiments corroborate our theoretical results.
Related Topics
Concepts
Finite element method
Convergence (economics)
Landau–Lifshitz–Gilbert equation
Mathematics
Magnetic field
Mathematical analysis
Range (aeronautics)
Euler's formula
Applied mathematics
Physics
Materials science
Quantum mechanics
Magnetization
Thermodynamics
Economics
Composite material
Economic growth
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2309.05530
- https://arxiv.org/pdf/2309.05530
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4386655633
All OpenAlex metadata
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https://openalex.org/W4386655633Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2309.05530Digital Object Identifier
- Title
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Stable $C^1$-conforming finite element methods for a class of nonlinear fourth-order evolution equationsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-09-11Full publication date if available
- Authors
-
Agus L. Soenjaya, Thanh TranList of authors in order
- Landing page
-
https://arxiv.org/abs/2309.05530Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2309.05530Direct 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/2309.05530Direct OA link when available
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Finite element method, Convergence (economics), Landau–Lifshitz–Gilbert equation, Mathematics, Magnetic field, Mathematical analysis, Range (aeronautics), Euler's formula, Applied mathematics, Physics, Materials science, Quantum mechanics, Magnetization, Thermodynamics, Economics, Composite material, Economic growthTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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