On high-order conservative finite element methods
This method addresses the need for locally conservative high-order approximations in subsurface flow simulations, but the improvement over existing methods is incremental.
The authors present a new high-order conservative finite element method for Darcy flow that achieves high-order convergence with locally conservative fluxes, applicable to highly heterogeneous problems in 3D.
A new high-order conservative finite element method for Darcy flow is presented. The key ingredient in the formulation is a volumetric, residual-based, based on Lagrange multipliers in order to impose conservation of mass that does not involve any mesh dependent parameters. We obtain a method with high-order convergence properties with locally conservative fluxes. Furthermore, our approach can be straightforwardly extended to three dimensions. It is also applicable to highly heterogeneous problems where high-order approximation is preferred.