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Stability and uniqueness results for a numerical approximation of the thermomechanical phase transitions in shape memory alloys. (English) Zbl 0826.65108
Summary: We consider a numerical scheme for the approximate solution of a coupled system of nonlinear partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys. It is shown that the solution to the scheme depends continuously upon the data. This immediately yields the uniqueness of the solution to the scheme. Finally we report some numerical results for load-driven and temperature-driven experiments for the shape memory alloy $$\text{Au}_{23} \text{Cu}_{30} \text{Zn}_{47}$$.

##### MSC:
 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35Q72 Other PDE from mechanics (MSC2000) 80A22 Stefan problems, phase changes, etc. 35R35 Free boundary problems for PDEs