A higher order nonconforming virtual element method for the Cahn-Hilliard equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929569849671680 |
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| author | Dedner, Andreas Hodson, Alice |
| author_facet | Dedner, Andreas Hodson, Alice |
| contents | In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error analysis for the semidiscrete (continuous-in-time) scheme and verify the theoretical convergence result via numerical experiments. We present a fully discrete scheme which uses a convex splitting Runge-Kutta method to discretize in the temporal variable alongside the virtual element spatial discretization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11408 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A higher order nonconforming virtual element method for the Cahn-Hilliard equation Dedner, Andreas Hodson, Alice Numerical Analysis 65M12, 65M60 In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error analysis for the semidiscrete (continuous-in-time) scheme and verify the theoretical convergence result via numerical experiments. We present a fully discrete scheme which uses a convex splitting Runge-Kutta method to discretize in the temporal variable alongside the virtual element spatial discretization. |
| title | A higher order nonconforming virtual element method for the Cahn-Hilliard equation |
| topic | Numerical Analysis 65M12, 65M60 |
| url | https://arxiv.org/abs/2111.11408 |