13th International Workshop on Variational Multiscale and Stabilized Finite Elemements (VMS 18) - Abstract
Nafa, Kamel
Mantle convection and melt migration are important processes for understanding Earth's dynamics and how they relate to the observations at the surface. Recent studies of geodynamics have shown that melt migration can be modeled by coupling variable-viscosity Stokes flow and Darcy flow. Where, Stokes flow, generally, captures the long-term behavior of the mantle and lithosphere while Darcy flow models the two-phase regime. Dannberg and Heister (2016) derived such a model for 2D and 3D simulations. However, the model they used require the so-called compaction pressure as an additional unknown in the system which does not only increases the dimension of the system, but also makes the underlying operator non-coercive. Approximating the solution using the finite element method requires the use of mixed inf-sup stable elements or additional stabilization terms. Here, we propose a formulation with a coercive non-symmetric linear operator which allow the use of simple equal-order elements.
This work was done in collaboration with Malte Braack and Simon Taylor from the University of Kiel, Germany.