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In this article, we develop a cut finite element method for one-phase Stefanproblems, with applications in laser manufacturing. The geometry of theworkpiece is represented implicitly via a level set function. Material abovethe melting/vaporisation temperature is represented by a fictitious gas phase.The moving interface between the workpiece and the fictitious gas phase may cutarbitrarily through the elements of the finite element mesh, which remainsfixed throughout the simulation, thereby circumventing the need for cumbersomere-meshing operations. The primal/dual formulation of the linear one-phaseStefan problem is recast into a primal non-linear formulation using aNitsche-type approach, which avoids the difficulty of constructing inf-supstable primal/dual pairs. Through the careful derivation of stabilisationterms, we show that the proposed Stefan-Signorini-Nitsche CutFEM method remainsstable independently of the cut location. In addition, we obtain optimalconvergence with respect to space and time refinement. Several 2D and 3Dexamples are proposed, highlighting the robustness and flexibility of thealgorithm, together with its relevance to the field of micro-manufacturing.

A CutFEM method for Stefan-Signorini problems with application in pulsed laser ablation