Three-field block-preconditioners for models of coupled magma/mantle dynamics

We discuss the iterative solution of a finite element discretisation of the magma dynamics equations.  These equations share features of the Stokes equations, however, Elman-Silvester-Wathen (ESW) preconditioners for the magma dynamics equations are not optimal. By introducing a new field, the compaction pressure, into the magma dynamics equations, we have developed a new three-field preconditioner which is optimal in terms of problem size and less sensitive to physical parameters compared to the ESW preconditioners.