Numerical Methods for a Nonconvex Optimization Problem Modeling Martensitic Microstructure

Using a continuum model of Ericksen and James, we compute a number of fine scale structures commonly observed as a result of martensitic phase transformations. Our results provide numerical validations of the Ericksen--James model. We show that care is needed in the discretization stage if spurious microstructures are to be avoided. A detailed description of the origin and cause of a spurious microstructure is provided. In addition, we present results showing the important effects of mesh orientation and mesh fineness on the formation of microstructure.