  In the flow and transport numerical simulation, mesh adaptivity strategy is
important in reducing the usage of CPU time and memory. The refinement based on
the pressure error estimator is commonly-used approach without considering the
flux error which plays important role in coupling flow and transport systems.
We derive a posteriori error estimators for Enhanced Velocity Mixed Finite
Element Method (EVMFEM) in the incompressible Darcy flow.
  We show numerically difference of the explicit residual based error estimator
and implicit error estimators, where Arbogast and Chen post-processing
procedure from [1] for pressure was used to improve estimators. A
residual-based error estimator provides a better indicator for pressure error.
Proposed estimators are good indicators in finding of the large error element.
Numerical tests confirm theoretical results. We show the advantage of pressure
postprocessing on the detecting of velocity error. To the authors' best
knowledge, a posteriori error analysis of EVMFEM has been scarcely investigated
from the theoretical and numerical point of view.
  Reference.
  1. Arbogast, T., & Chen, Z. (1995). On the implementation of mixed methods as
nonconforming methods for second-order elliptic problems. Mathematics of
Computation, 64(211), 943-972.

Numerical Analysis;Numerical Analysis