講座主題：A constrained transport divergence-free finite element method for incompressible MHD equations
專(zhuān)家姓名：鄭偉英
工作單位：中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院
講座時(shí)間：2022年6月13日 15:00-16:30
講座地點(diǎn)：騰訊會(huì)議：168 518 977
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員，主要從事有限元方法的理論與應(yīng)用研究，包括電磁和流體計(jì)算等，在Maxwell方程自適應(yīng)多重網(wǎng)格方法的最優(yōu)收斂性、分層介質(zhì)散射問(wèn)題以及三維磁流體計(jì)算等方面取得重要研究進(jìn)展。2017年獲國(guó)家杰出青年科學(xué)基金資助，2019年任中科院數(shù)學(xué)與系統(tǒng)科學(xué)研究院“馮康首席研究員”，2021年獲馮康科學(xué)計(jì)算獎(jiǎng)。
