Workshop on Numerical Methods and Analysis in CFD - Abstract
Jha, Abhinav
Non-linear discretizations are necessary for convection-diffusion reaction equations for obtaining accurate solutions that satisfy the discrete maximum principle (DMP). Algebraic stabilizations belong to the very few finite element discretizations that satisfy this property.
In this talk, we consider three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the AFC scheme with BJK limiter BJKR18.SeMa, and the recently proposed Monotone Upwind-type Algebraically Stabilized (MUAS) method JK21.arXiv. Both, conforming closure of the refined grids and grids with hanging vertices are considered based on a residual-based a posteriori error estimator proposed in Jha21.CAMWA.
A non-standard algorithmic step becomes necessary before these schemes can be applied on grids with hanging vertices. The assessment of the schemes is performed with respect to the satisfaction of the global discrete maximum principle (DMP), the accuracy, e.g., smearing of layers, and the efficiency in solving the corresponding nonlinear problems.