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Time Discretisation for a Class of Singular Phase Field Models
This paper is motivated by the work of Bonetti, Colli, Fabrizio and Gilardi (J. Differential Equations 2009;246;3260-3295), which treats the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law.
Our main purpose is to discretise this model in time, show the existence, uniqueness and boundedness of the order parameter $\chi$ for the discretised model. Finally, the paper gives a result on the convergence of the discretised model to the time continuous one.