Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical model- ing of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover global pressure. A combination of a discontinuous Galerkin method for the advection equa- tions and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D. A projective and adaptively applied pressure estimation is employed to significantly reduce the compu- tational wall time without impacting the overall physical reliability in the modeling of important features of melt and segregation, such as melt channel bifurcation in 2D and 3D time dependent simulations.