报告主题：自适应多层混合有限元方法
报告人：胡俊 教授 （北京大学）
报告时间：2017年 10月13日（周五）16:00
报告地点：校本部G508
邀请人：刘东杰
主办部门：8455新葡萄场网站数学系
报告摘要：In the first part, we developed a block diagonal preconditioner with the minimal residual method and a block triangular preconditioner with the generalized minimal residual method for the mixed finite element methods of linear elasticity. They are based on a new stability result of the saddle point system in mesh-dependent norms. The mesh-dependent norm for the stress corresponds to the mass matrix which is easy to invert while the displacement it is spectral equivalent to Schur complement. A fast auxiliary space preconditioner based on the H1 conforming linear element of the linear elasticity problem is then designed for solving the Schur complement. For both diagonal and triangular preconditioners, it is proved that the conditioning numbers of the preconditioned systems are bounded above by a constant independent of both the crucial Lame constant and the mesh-size. Numerical examples are presented to support theoretical results.
In the second part, we proposed a posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions. In particular, we proved reliability and efficiency of the estimators.
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