Rodolfo Araya, Abner Poza, Frederic Valentin:
On a hierarchical estimator driven by a stabilized method for the reactive incompressible Navier-Stokes equations
This work concerns with compounding two complementary strategies to accurately solve the reactive incompressible Navier-Stokes model, namely, a stabilized method and a mesh refinement approach relied on an error estimator. We adopt equal order interpolation spaces to approach both the velocity and the pressure, and the stability is recovered from a new unusual stabilized finite element method. The method is designed to deal with reactive and advective dominate flows through a threefold asymptotic behavior of the stabilization parameter. Mesh adaptivity driven by a new hierarchical error estimator and built on the unusual method is the second ingredient. The estimator circumvents the saturation assumption by using an enhanced space strategy and shows to be equivalent to the error. Several numerical tests validate the combined methodology.
This preprint gave rise to the following definitive publication(s):
Rodolfo ARAYA, Abner POZA, Frederic VALENTIN: On a hierarchical error estimator combined with a stabilized method for the Navier–Stokes equations. Numerical Methods for Partial Differential Equations, vol. 28, 3, pp. 782–806, (2012).