A Lecture by Prof. Long Chen on “Multigrid Methods for Saddle Point Systems of Mixed Finite Element Methods”
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A Lecture by Prof. Long Chen on “Multigrid Methods for Saddle Point Systems of Mixed Finite Element Methods”
DateandTime: 2015-12-29 10:03:15

Speaker: Long Chen, associate professor at University of California, Irvine, USA

Date: December 29, 2015

Time: 10:00 a.m.-11:00 a.m.

Location: Room B1032, Zhixin Building, Central Campus

Sponsor: the School of Mathematics


The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace optimization method based on a multilevel decomposition of the constraint space. Convergence theory is developed for successive subspace optimization methods based on two assumptions on the space decomposition: stable decomposition and strengthened Cauchy-Schwarz inequality, and successfully applied to the saddle point systems arising from mixed finite element methods for Poisson, Stokes equations, and plate bending problems. Uniform convergence is obtained without the full regularity assumption of the underlying partial differential equations. Exact sequences of Hilbert complexes plays an important role in the design and analysis of our method.


Dr. Long Chen is Associate Professor of University of California, Irvine. He completed his Ph.D. from Pennsylvania State University in 2005. His research interests include Numerical Solution of PDEs, Adaptive Finite Element Method, Grid Generation, Multigrid. 

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Edited by: Li Ao

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