International conference on Advances in Differential Equations and Numerical Analysis, Guwahati, India, 12 - 15 October 2020, pp.279
In this talk, we are interested in the numerical solution of convection-dominated models with nonlinear reaction mechanisms. The existence of the advection term(s) in the relevant models causes the
numerical solutions obtained by standard methods to exhibit nonphysical oscillations. Therefore, the
Galerkin finite element method (GFEM) is stabilized using the Streamline-Upwind/Petrov-Galerkin
(SUPG) technique to prevent spurious oscillations. Moreover, the stabilized formulation is enhanced
by the YZβ shock-capturing technique. Finally, the proposed numerical scheme is tested on various
reaction models. All the numerical computations are performed in the FEniCS environment.