Bo Li's Past Research

Continuum models, theory, and simulation of epitaxial growth of thin films: growth instabilities, coarsening and dynamic scaling, roughening transition, stress effects, electromigration, nanoscale pattern formation, numerical simulation, etc.
- Some related work
  1. Russel E. Caflisch and Bo Li, Analysis of island dynamics in epitaxial growth of thin films, Multiscale Model. Simul., 1(1):150-171, 2003.
  2. Bo Li and Jian-Guo Liu, Thin film epitaxy with or without slope selection, European J. Appl. Math., 14(6):713-743, 2003.
  3. Eberhard Bänsch, Frank Hausser, Omar Lakkis, Bo Li, and Axel Voigt, Finite elment methods for epitaxial growth with attachment-detachment kinetics, J. Comput. Phys., 194(2):409-434, 2004.
  4. Bo Li, Andreas Rätz, and Axel Voigt, Stability of a circular epitaxial island, Physica D, 198:231-247, 2004.
  5. Bo Li and Jian-Guo Liu, Epitaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., 14:429-451, 2004.
  6. Bo Li, High-order surface relaxation vs. the Ehrlich-Schwoebel effect, Nonlinearity, 19(11):2581-2603, 2006.
- A list of references.
Stress-driven interface dynamics with applications to nanoscale structures
- Collaborative Research: Hybrid Finite-Element Level-Set Methods for Stress-Driven Interface Dynamics, PI, NSF, grant DMS-0451466, 7/1/04 - 6/30/07. Project abstract.
- Some recent work
  1. Xingzhou Yang, Bo Li, and Zhilin Li, The immersed interface method for elasticity problems with interfaces, Dyn. Contin. Discrete Impuls. Syst. Ser. A: Math. Anal., 10(5):783-808, 2003.
  2. Yan Gong, Bo Li, and Zhilin Li, Immersed-interface finite-element method for elliptic interface problems with non-homogeneous jump conditions, SIAM J. Numer. Anal., 46(1):472-495, 2008.
  3. Jérôme Colin, Bo Li, and Qing Nie, Surface evolution of epitaxially strained multi-layers with dipoles of edge dislocations (in preparation).
- A list of references to the stress-induced morphological instabilities: html file.
Modeling, simulation, and analysis of complex martensitic microstructures - with an emphasis on the effect of applied stress to formation, evolution, and stability of the microstructure.
- Some related work
  1. Bo Li and Mitchell Luskin, Finite element analysis of microstructure for the cubic to tetragonal transformation, SIAM J. Numer. Anal., 35(1):376-392, 1998.
  2. Bo Li and Mitchell Luskin, Nonconforming finite element approximation of crystalline microstructure, Math. Comp., 67(223):917-946, 1998.
  3. Bo Li and Mitchell Luskin, Approximation of a martensitic laminate with varying volume fractions, ESAIM: Math. Model. Numer. Anal., 33(1):67-87, 1999.
  4. Kaushik Bhattacharya, Bo Li, and Mitchell Luskin, The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation, Arch. Rational Mech. Anal., 149(2), 123-154, 1999.
  5. Bo Li and Mitchell Luskin, Theory and computation for the microstructure near the interface between twinned layers and a pure variant of martensite, Materials Sci. Eng. A, 273:237-240, 1999.
  6. Bo Li, Approximation of martensitic microstructure with general homogeneous boundary data, J. Math. Anal. Appl., 266:451-467, 2002.
  7. Bo Li, Finite element analysis of a class of stress-free martensitic microstructures, Math. Comp., 72(244):1675-1688, 2003.
- Some pictures of computer simulated martensitic microstructure reproduced from Bo Li's Ph.D. thesis: Analysis and computation of martensitic microstructure, University of Minnesota, 1996. Thesis advisor: Professor Mitchell B. Luskin.
- A list of references to the numerical computation of crystalline microstructure and the related numerical analysis of nonconvex variational problems: ps file; pdf file.
- Martensite on the web
Weak convergence methods for variational problems modeling crystalline solids that can undergo structural phase transformations
- Description of a related applied mathematics course for graduate students, UCLA, 1998: html file, ps file, pdf file.
- References to weak topology methods for varitional problems modeling crystalline microstructure. A short list: ps file; pdf file. A long list: ps file; pdf file.
Superconvergence analysis and a posteriori error estimates in the adaptive finite element method - An effort will be made to lift the severe restrictions on finite element meshes in achiving the superconvergence, and an emphasis will be placed on the study of moving boundary problems and multiscale problems with applicatons to materials science.

Related publications
1. Bo Li, Superconvergence for higher-order triangular finite elements, Chinese J. Numer. Math. & Appl., 12(1):75-79, 1990.
2. Hongsen Chen and Bo Li, Superconvergence analysis and error expansion for the Wilson nonconforming finite element, Numer. Math., 69(2):125-140, 1994.
3. Bo Li and Zhimin Zhang, Analysis of a class of superconvergence patch recovery techniques for linear and bilinear finite elements, Numer. Methods for PDEs, 15:151-167, 1999.
4. Bo Li, Lagrange interpolation and finite element superconvergence, Numer. Methods for PDEs, 20(1):33-59, 2004.