A Stabilized Unfitted Space-time Finite Element Method for Parabolic Problems on Moving Domains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915907461185536 |
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| author | Wang, Ruizhi Deng, Weibing |
| author_facet | Wang, Ruizhi Deng, Weibing |
| contents | This paper presents a space-time finite element method (FEM) based on an unfitted mesh for solving parabolic problems on moving domains. Unlike other unfitted space-time finite element approaches that commonly employ the discontinuous Galerkin (DG) method for time-stepping, the proposed method employs a fully coupled space-time discretization. To stabilize the time-advection term, the streamline upwind Petrov-Galerkin (SUPG) scheme is applied in the temporal direction. A ghost penalty stabilization term is further incorporated to mitigate the small cut issue, thereby ensuring the well-conditioning of the stiffness matrix. Moreover, an a priori error estimate is derived in a discrete energy norm, which achieves an optimal convergence rate with respect to the mesh size. In particular, a space-time Poincare-Friedrichs inequality is established to support the condition number analysis. Several numerical examples are provided to validate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stabilized Unfitted Space-time Finite Element Method for Parabolic Problems on Moving Domains Wang, Ruizhi Deng, Weibing Numerical Analysis This paper presents a space-time finite element method (FEM) based on an unfitted mesh for solving parabolic problems on moving domains. Unlike other unfitted space-time finite element approaches that commonly employ the discontinuous Galerkin (DG) method for time-stepping, the proposed method employs a fully coupled space-time discretization. To stabilize the time-advection term, the streamline upwind Petrov-Galerkin (SUPG) scheme is applied in the temporal direction. A ghost penalty stabilization term is further incorporated to mitigate the small cut issue, thereby ensuring the well-conditioning of the stiffness matrix. Moreover, an a priori error estimate is derived in a discrete energy norm, which achieves an optimal convergence rate with respect to the mesh size. In particular, a space-time Poincare-Friedrichs inequality is established to support the condition number analysis. Several numerical examples are provided to validate the theoretical findings. |
| title | A Stabilized Unfitted Space-time Finite Element Method for Parabolic Problems on Moving Domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.10242 |