Assistant Professor Bo Li

Bo Li will be coming to us from UCLA as an assistant professor. He will be on leave from Maryland in 1998-99 in order to remain at UCLA for one more year. This year he will be teaching the Applied Numerical Analysis sequence at UCLA, continuing his research on mathematical problems in materials science, and visiting a number of collaborators.

• Numerical analysis and scientific computation.
• Nonlinear partial differential equations and direct methods in the calculus of variations.
• Linear and nonlinear elasticity, mechanics and physics of crystalline solids, and fluid mechanics.
• Mathematical aspects of materials science.

• Virtual integrated prototyping for epitaxial growth - a project on thin films.
• Numerical simulation of crystalline microstructure and the related numerical analysis of non-convex variational problems.
      Here are some pictures of computer simulated martensitic microstructure reproduced from Bo Li's Ph.D. thesis (University of Minnesota, 1996).
  • twin branching
  • bent needles
  • multiple generations of twins
• Weak topology methods for variational problems modeling crystalline solids.
• Superconvergence analysis and a posteriori error estimates in the adaptive finite element method.

1. A Convergence analysis of the Wilson nonconforming finite element (in Chinese), Chinese first national conference on numerical solutions of partial differential equations, Shanghai, China (1987), collected in the book Superconvergence Theory of Finite Elements by Qiding Zhu and Qun Lin (1989), translated into English (1995).
2. Superconvergence for higher-order triangular finite elements, Chinese J. Numer. Math. & Appl. 12:1 (1990), 75-79.
3. Superconvergence analysis and error expansion for the Wilson nonconforming finite element, Numer. Math. 69:2 (1994), 125-140 (with Hongsen Chen).
4. Analysis of a class of nonconforming finite elements for crystalline microstructures, Math. Comp. 65:215 (1996), 1111-1135 (with Petr Kloucek and Mitchell Luskin).
5. Analysis and computation of martensitic microstructure, Ph.D Thesis, University of Minnesota, 1996.
6. Finite element analysis of microstructure for the cubic to tetragonal transformation, SIAM J. Numer. Anal. 35:1 (1998), 376-392 (with Mitchell Luskin).
7. Nonconforming finite element approximation of crystalline microstructure, Math. Comp. 67 (1998), 917-946. (with Mitchell Luskin).
8. Approximation of a martensitic laminate with varying volume fractions, to appear in Math. Model. Numer. Anal. (with Mitchell Luskin).
9. Analysis of a class of superconvergence patch recovery techniques for linear and bilinear finite elements, UCLA CAM report, 97-8, March, 1997 (with Zhimin Zhang).
10. On the existence of finite element minimizers, UCLA CAM report, 97-45, September, 1997 (with Mitchell Luskin).
11. Numerical simulation of needle-like microstructure in martensitic crystals, manuscript, 1997 (with Mitchell Luskin).
12. Uniqueness and stability of the simply laminated microstructure for martensitic crystals that undergo a cubic to orthorhombic phase transformation, UCLA CAM report, 98-26, 1998 (with Kaushik Bhattacharya and Mitchell Luskin).