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Mass Conservative Domain Decomposition for Porous Media Flow

Understanding flow in subsurface porous media is of great importance for society due to applications such as energy extraction and waste disposal. The governing equations for subsurface flow are a set of non-linear partial differential equations of mixed elliptichyperbolic type, and the parameter fields are highly heterogeneous with characteristic features on a continuum of length scales. This calls for robust discretization methods that balance the challenges in designing efficient and accurate methods. In this chapter we focus on a class of linear solvers for elliptic systems that aims at providing fast approximate solutions, preferably in one iteration, but fall back to being iterative methods with good convergence properties if higher accuracy is needed.