Istituto di Matematica Applicata e Tecnologie Informatiche     
Stefanelli U. Error control of a nonlinear evolution problem related to phase transitions. Preprint ercim.cnr.ian//1999-1130, 1999.
In this paper we study a time discretization with variable time step of a nonlinear evolution problem which describes the behaviour of materials subjected to multi-component phase transitions with dissipation. Existence and uniqueness of solutions to this model have been investigated in [8] by using a time discretization approach. Nevertheless, no error estimates for the discretization error were shown in [8]. Here, the existence of the solution is recovered by passing to the limit in a new variable step time discretization. Then, optimal order a priori error estimates of the discretization error are shown. These estimates depend solely on data and no constraint is imposed between consecutive time steps.
Subject Nonlinear evolution problem, phase transitions, time discretization, convergence results, error estimates
35K55, 65M12, 65M15

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