Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910280441659392 |
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| author | Bullerjahn, Nils |
| author_facet | Bullerjahn, Nils |
| contents | A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy estimate and the novel approach of exploiting the almost mass conservation of the error equations to derive a Poincaré-type inequality. We demonstrate how this approach can be generalized to other almost mass conserving problems. To this end we prove optimal-order fully discrete error estimates for the Cahn--Hilliard equation on evolving surfaces. We illustrate and complement our findings by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions Bullerjahn, Nils Numerical Analysis A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy estimate and the novel approach of exploiting the almost mass conservation of the error equations to derive a Poincaré-type inequality. We demonstrate how this approach can be generalized to other almost mass conserving problems. To this end we prove optimal-order fully discrete error estimates for the Cahn--Hilliard equation on evolving surfaces. We illustrate and complement our findings by numerical experiments. |
| title | Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.03847 |