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A new enriched finite element formulation for solving isothermal phase change problems is presented.We propose a xed mesh method, where the discontinuity in the temperature gradient is representedby enriching the nite element space through a function whose denition includes a gradient discontinuity. Generally, in these types of formulations, the enrichment location (the location of the solidication front) is determined through a level set auxiliary scheme. In this work, this position is determined implicitly by constraining the temperature at the phase change boundary to be equal to the melting temperature. Several numerical examples are presented to show the application of the method.