Unstructured tetrahedral mesh adaptation for two-dimensional space-time finite elements

Space-time finite elements in two dimensions require the construction of a three-dimensional mesh within each time slab. To control the accuracy of the transient solution, mesh adaptation of the time slabs usually implies the interpolation of the solution at the interface between the current and the previous time slabs. Such interpolation introduces excessive diffusion for transient solution. The approach proposed in this paper is to adapt the mesh inside the time slab, with the restriction that the twodimensional unstructured triangular mesh at the bottom of the time slab (previous time level) must be unmodified. This eliminates the interpolation of the solution and the diffusion it produces.

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