講座主題：A constrained transport divergence-free finite element method for incompressible MHD equations
專家姓名：鄭偉英
工作單位：中國科學院數學與系統科學研究院
講座時間：2022年6月13日 15:00-16:30
講座地點：騰訊會議：168 518 977
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
We study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method, we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom. A comparison with other discretization using lid driven cavity is also given.
主講人介紹：
鄭偉英，中國科學院數學與系統科學研究院研究員，主要從事有限元方法的理論與應用研究，包括電磁和流體計算等，在Maxwell方程自適應多重網格方法的最優收斂性、分層介質散射問題以及三維磁流體計算等方面取得重要研究進展。2017年獲國家杰出青年科學基金資助，2019年任中科院數學與系統科學研究院“馮康首席研究員”，2021年獲馮康科學計算獎。
