2017/01/30 by Abreu, Eduardo, Diaz, Ciro, Galvis, Juan +1
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1701.08855
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.