An error estimate for structure-preserving finite difference scheme for the Falk model system of shape memory alloys

作者：Yoshikawa Shuji^*

来源：IMA Journal of Numerical Analysis, 2017, 37(1): 477-504.

DOI：10.1093/imanum/drv072

• finite difference method
• discrete variational derivative method
• Falk's model
• shape memory alloys
• thermoelastic system

The Falk model is a thermoelastic system describing the phase transition occurring in shape memory alloys. In an earlier paper [Yoshikawa, S. (2015) Aconservative finite difference scheme for the Falk model system of shape memory alloys. Zeitschrift fur Angewandte Mathematik und Mechanik, 95(12), 1393-1410], the author proposed a structure-preserving finite difference scheme for the Falk model system, and proved the existence of a solution for the implicit numerical scheme. Here, we give a different existence proof from the one in that paper by using the energy method. In addition, we prove a bound on the error between the numerical solution and the analytical solution.

• 出版日期2017-1