The problems that are most frequently solved in scientific and engineering computing may probably be the elasticity equations. The finite element method (FEM) was invented in analyzing the stress of the elastic structures in the 1950s. The mixed FEM within the Hellinger-Reissner (H-R) principle for elasticity yields a direct stress approximation since it takes both the stress and displacement as an independent variable. The mixed FEM can be free of locking for nearly incompressible materials, and be applied to plastic materials, and approximate both the equilibrium and traction boundary conditions more accurate. However, the symmetry of the stress plus the stability conditions make the design of the mixed FEM for elasticity surprisingly hard.
The talk presents a new framework to design and analyze the mixed FEM of elasticity problems, which yields optimal symmetric mixed FEMs. In addition, those elements are very easy to implement since their basis functions, based on those of the scalar Lagrange elements, can been explicitly written down by hand. The main ingredients of this framework are a structure of the discrete stress space on both simplicial and product grids, two basic algebraic results, and a two-step stability analysis method.
The talk presents a new framework to design and analyze the mixed FEM of elasticity problems, which yields optimal symmetric mixed FEMs. In addition, those elements are very easy to implement since their basis functions, based on those of the scalar Lagrange elements, can been explicitly written down by hand. The main ingredients of this framework are a structure of the discrete stress space on both simplicial and product grids, two basic algebraic results, and a two-step stability analysis method.
3 Jan 2020
11:00am - 12:00pm

Where
Room 3472, Academic Building (Lifts 25-26)
Speakers/Performers
Prof. Jun HU
Peking University
Peking University
Organizer(S)
Department of Mathematics
Contact/Enquiries
mathseminar@ust.hk
Payment Details
Audience
Alumni, Faculty and Staff, PG Students, UG Students
Language(s)
English
Other Events

24 Mar 2025
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Pushing the Limit of Nonlinear Vibrational Spectroscopy for Molecular Surfaces/Interfaces Studies
Abstract
Surfaces and interfaces are ubiquitous in Nature. Sum-frequency generation vibrational spectroscopy (SFG-VS) is a powerful surface/interface selective and sub-monolayer sensitive spect...

22 Nov 2024
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Leveraging Protein Dynamics Memory with Machine Learning to Advance Drug Design: From Antibiotics to Targeted Protein Degradation
Abstract
Protein dynamics are fundamental to protein function and encode complex biomolecular mechanisms. Although Markov state models have made it possible to capture long-timescale protein co...