  In this work we use algebraic dual representations in conjunction with domain
decomposition methods for Darcy equations. We define the broken Sobolev spaces
and their finite dimensional counterparts. In addition, a global trace space is
defined that connects the solution between the broken spaces. Use of dual
representations results in a sparse metric free representation of the
constraint on divergence of velocity, the pressure gradient term and on the
continuity constraint across the sub domains. To demonstrate this, we solve two
test cases: i) manufactured solution case, and ii) industrial benchmark
reservoir modelling problem SPE10. The results demonstrate that the domain
decomposition scheme, although with more unknowns, requires less memory and
simulation time as compared to the continuous Galerkin formulation.
