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| Autores principales: | , , , |
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| Formato: | Artículo Open Access |
| Publicado: |
Wiley
2025
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| Materias: | |
| Acceso en línea: | https://onlinelibrary.wiley.com/doi/10.1002/num.70052 |
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- A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema Gang Wang Mingchao Cai Xiaojing Dong Yinnian He Numerical Methods for Partial Differential Equations ABSTRACT In this study, we introduce a mixed virtual element method (VEM) for the approximation of the poroelasticity problem on polygonal meshes. For the continuous formulation, we consider a four‐field formulation in which the primal unknown variables are the total stress and displacement and the fluid flux and pressure. In the proposed virtual element method, a mixed virtual element with a priori symmetric stress is used to approximate the total stress and displacement, whereas a Raviart–Thomas type mixed virtual element is applied for the approximation of the fluid flux and pressure. When employing backward Euler time stepping, we construct a fully discrete scheme for the poroelasticity problem. Subsequently, the well‐posedness and optimal a priori error estimates are established for the fully discrete scheme. We provide numerical results that corroborate the theoretical findings. Additionally, we apply the proposed method to simulate brain edema. 10.1002/num.70052 http://onlinelibrary.wiley.com/termsAndConditions#vor