Numerische Mathematik

, Volume 89, Issue 3, pp 511–533 | Cite as

A mesh transformation method for computing microstructures

  • Zhiping Li
Original article


A numerical method is established to solve the problem of minimizing a nonquasiconvex potential energy. Convergence of the method is proved both in the case on its own and in the case when it is combined with a weak boundary condition. Numerical examples are given to show that the method, especially when applied together with a continuation method and some other numerical techniques, is not only successful and efficient in solving problems with laminated microstructures but also capable of computing more complicated microstructures.

Mathematics Subject Classification (1991): 65K10, 65N12, 65N30, 49J45, 49M20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Zhiping Li
    • 1
  1. 1.School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China; e-mail: CN

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