An error estimate for structure-preserving finite difference scheme for the Falk model system of shape memory alloys
Shuji Yoshikawa · IMA Journal of Numerical Analysis · 2016
The Falk model is a thermoelastic system describing the phase transition occurring in shape memory alloys. In an earlier paper [Yoshikawa, S. (2015) A conservative finite difference scheme for the Falk model system of shape memory alloys. Zeitschrift für 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.