2017年11月20日 |  English version
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重点实验室专题报告——Mixed Finite Element Methods based on Differential Complexes

报告题目:Mixed Finite Element Methods based on Differential Complexes

报告人: Prof. Long Chen, University of California at Irvine & Beijing Institute for Scientific and Engineering Computing

报告时间:201773(周一)  15:00

报告地点:行健楼学术报告室526

邀请人:王锋副教授

Abstract We shall present a systematically study of the mixed finite element methods based on differential complexes and the corresponding Helmholtz decomposition. Firstly, we use the differential complexes to construct fast solvers for the saddle point systems arising from the mixed finite element methods. We discuss two type of fast solvers: Constraint optimization methods: Darcy equations, Stokes equations, and Kirchhoff plate bending problems.  Preconditioners based on approximated block factorization: the Hodge Laplacian, Maxwell and the linear elasticity equations. Secondly, we analyze adaptive finite element methods based on the differential complexes. In particular, we discuss  - A posterior error estimates for symmetric conforming mixed finite elements for linear elasticity Convergence of adaptive mixed finite element methods for the Hodge Laplacian equations. Finally, we utilize the Helmholtz decomposition to decouple the mixed formulation of high order elliptic equations into combination of Poisson-type and Stokes-type equations. Examples include but not limit to: the biharmonic equation, the tri-harmonic equation, the fourth order curl equation, HHJ mixed method for plate problem, and Reissner-Mindlin plate model etc.

 

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