A posteriori error estimates of Darcy flows with Robin-type jump interface conditions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929629261987840 |
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| author | Lee, Jeonghun J. |
| author_facet | Lee, Jeonghun J. |
| contents | In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott--Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14287 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A posteriori error estimates of Darcy flows with Robin-type jump interface conditions Lee, Jeonghun J. Numerical Analysis 65N30, 65N15 In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott--Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included. |
| title | A posteriori error estimates of Darcy flows with Robin-type jump interface conditions |
| topic | Numerical Analysis 65N30, 65N15 |
| url | https://arxiv.org/abs/2304.14287 |