  This article considers the iterative solution of a finite element
discretisation of the magma dynamics equations. In simplified form, the magma
dynamics equations share some features of the Stokes equations. We therefore
formulate, analyse and numerically test a Elman, Silvester and Wathen-type
block preconditioner for magma dynamics. We prove analytically and demonstrate
numerically the optimality of the preconditioner. The presented analysis
highlights the dependence of the preconditioner on parameters in the magma
dynamics equations that can affect convergence of iterative linear solvers. The
analysis is verified through a range of two- and three-dimensional numerical
examples on unstructured grids, from simple illustrative problems through to
large problems on subduction zone-like geometries. The computer code to
reproduce all numerical examples is freely available as supporting material.
