FINITE-ELEMENT APPROXIMATIONS OF LANDAU-GINZBURGS EQUATION MODEL FOR STRUCTURAL PHASE-TRANSITIONS IN SHAPE-MEMORY ALLOYS

This paper deals with finite element approximations of the Landau-Ginz burg model for structural phase transitions in shape memory alloys. ri le non-linear evolutionary system of partial differential equations is discretized in time by finite differences and in space by very simple finite elements, that is, the linear element for the absolute tempera ture and the Hermite cubic element for the displacement. Thus both the displacement and tile strain are obtained directly. Error estimates f or the fully discrete scheme are derived.