تقرير
Space-Time CutFEM on Overlapping Meshes: Simple Continuous Mesh Motion
| العنوان: | Space-Time CutFEM on Overlapping Meshes: Simple Continuous Mesh Motion |
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| المؤلفون: | Larson, Mats G., Logg, Anders, Lundholm, Carl |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65M60, 65M85, 65M12, 65M22 |
| الوصف: | We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that moves around inside/"on top" of it. Here the overlapping mesh is prescribed a simple continuous motion, meaning that its location as a function of time is continuous and piecewise linear. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche's method and also includes an integral term over the space-time boundary between the two meshes that mimics the standard discontinuous Galerkin time-jump term. The simple continuous mesh motion results in a space-time discretization for which standard analysis methodologies either fail or are unsuitable. We therefore employ what seems to be a relatively new energy analysis framework that is general and robust enough to be applicable to the current setting. The energy analysis consists of a stability estimate that is slightly stronger than the standard basic one and an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders. Comment: Preprint for journal submission. arXiv admin note: text overlap with arXiv:2301.13517 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.00337 |
| رقم الأكسشن: | edsarx.2302.00337 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |