Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 王飞 副教授,西安交通大学数学与统计学院
| | Inviter: | | Title:
| Mixed Discontinuous Galerkin Method for Brinkman Problem | Time & Venue:
| 2021.11.25 09:30-10:30 腾讯会议ID：207 227 830 | Abstract:
| 会议链接：https://meeting.tencent.com/dm/G0eC6rUYX5lJ
The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy's law). The numerical challenge for this model is the designing of a numerical scheme which is stable for both the Stokes- dominated (high permeability) and the Darcy-dominated (low permeability) equations. In this talk, we discuss the Brinkman model in n dimensions (n = 2, 3) by using the mixed discontinuous Galerkin (MDG) method, which meets this challenge. This MDG method is based on the stress-velocity formulation and uses a discontinuous piecewise polynomial pair, where the stress field is symmetric. The main unknowns are the stress and the velocity, whereas the pressure is easily recovered through a simple postprocessing. A key step in the analysis is to establish the parameter-robust inf-sup stability through specific parameter-dependent norms at both continuous and discrete levels. Therefore, the stability results presented here are uniform with respect to the permeability. Thanks to the parameter-robust stability analysis, we obtain optimal error estimates for the stress in broken H(div)-norm and velocity in L2-norm. Furthermore, the L2 error estimate for stress is derived under certain conditions. Finally, numerical experiments are provided to support the theoretical results and to show the robustness, accuracy, and flexibility of the MDG method.
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