A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System
This paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the problem defining the interaction between a free fluid and poroelastic structure. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/7472965 |
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| _version_ | 1832564901238800384 |
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| author | Koffi Wilfrid Houédanou |
| author_facet | Koffi Wilfrid Houédanou |
| author_sort | Koffi Wilfrid Houédanou |
| collection | DOAJ |
| description | This paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the problem defining the interaction between a free fluid and poroelastic structure. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain. For this discretization, we derive a residual indicator based on the jumps of the normal derivative of the nonconforming approximation. Lower and upper bounds form the main results with minimal assumptions on the mesh. |
| format | Article |
| id | doaj-art-9a46aa9cf9634ef7a5005494562437bb |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-9a46aa9cf9634ef7a5005494562437bb2025-02-03T01:09:52ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/7472965A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot SystemKoffi Wilfrid Houédanou0Université D’abomey-Calavi (UAC)This paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the problem defining the interaction between a free fluid and poroelastic structure. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain. For this discretization, we derive a residual indicator based on the jumps of the normal derivative of the nonconforming approximation. Lower and upper bounds form the main results with minimal assumptions on the mesh.http://dx.doi.org/10.1155/2022/7472965 |
| spellingShingle | Koffi Wilfrid Houédanou A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System Discrete Dynamics in Nature and Society |
| title | A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System |
| title_full | A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System |
| title_fullStr | A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System |
| title_full_unstemmed | A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System |
| title_short | A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System |
| title_sort | posteriori error estimates for a nonconforming finite element discretization of the stokes biot system |
| url | http://dx.doi.org/10.1155/2022/7472965 |
| work_keys_str_mv | AT koffiwilfridhouedanou aposteriorierrorestimatesforanonconformingfiniteelementdiscretizationofthestokesbiotsystem AT koffiwilfridhouedanou posteriorierrorestimatesforanonconformingfiniteelementdiscretizationofthestokesbiotsystem |