Numerical computation of the free boundary for the two-dimensional Stefan problem by space-time finite elements

Abstract We describe a finite element method for the numerical solution of the two-dimensional Stefan problem. At each time step, the free boundary is approximated by a polygonal line whose vertices coincide with triangulation nodes. This is achieved by using space-time finite elements, which allow a change in the position of the nodes at each time step. Numerical results are given.

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