Simplex space–time meshes in finite element simulations

A straightforward method for generating simplex space-time meshes is presented, allowing arbitrary temporal refinement in selected portions of space-time slabs. The method increases the flexibility of space-time discretizations, even in the absence of dedicated space-time mesh generation tools. The resulting tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes are tested in the context of advection-diffusion equation, and are shown to provide reasonable solutions, while enabling varying time refinement in portions of the domain.

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