Space-Time mesh adaptation for solving the Porous Medium Equation
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In this contribution, we propose to generate adaptive space-time meshes to capture fronts. As a toy problem, we use the Porous Medium Equation (PME) that is a non-linear partial differential equation of significant interest due to its widespread applicability in modelling various physical phenomena such as gas flow in porous medium, incompressible fluid dynamics and non-linear heat transfer. In this paper, we compute The PME using a space-time formulation. We focus on the 2D computation in space plus time. In each time step, we use the relaying technique to capture the mesh in space. Tetrahedra connect the different spatial planes and the tetrahedral mesh is adapted to capture the exact front in space and time, leading to a mimetic representation of the front.