Error indicators for incompressible Darcy Flow problems using Enhanced Velocity Mixed Finite Element Method

Abstract

Local mesh adaptivity serves as a practical tool in numerical simulations to accurately capture features of interest while reducing computational time and memory requirements. In this work, we suggest a refinement strategy based on pressure and flux error estimates for numerical simulation of an incompressible, single phase flow and transport process in the subsurface porous media. We derive a posteriori error estimates for an Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a spatial domain decomposition approach. We note that the flux errors play an important role in coupled flow and transport systems later demonstrated using numerical experiments. A comparison between explicit (residual based) error estimators and an implicit error estimator; based upon the post-processing proposed by Arbogast and Chen (1995), shows that the latter performs better. A residual-based error estimator for pressure was found to be both computationally efficient while sufficiently indicating the large error subdomains. Numerical studies are also presented that confirm our theoretical derivations while demonstrating the advantages of post-processing in detecting velocity errors.