A conservative hybrid method for Darcy flow
It provides a computationally efficient numerical method for solving Darcy flow problems in porous media.
The paper introduces a hybrid mimetic spectral element method for Darcy flow that yields extremely sparse matrix systems, enabling efficient element-wise assembly and solution.
We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for 1) conservation of mass, and 2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately.