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A mesh transformation method for computing microstructures

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Summary.

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.

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Received March 17, 2000 / Published online April 5, 2001

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Li, Z. A mesh transformation method for computing microstructures. Numer. Math. 89, 511–533 (2001). https://doi.org/10.1007/PL00005477

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  • DOI: https://doi.org/10.1007/PL00005477

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