Adapted numerical modeling for advection-reaction-diffusion problems on a bidimensional spatial domain

The paper provides an adapted numerical scheme for advectionreaction-diffusion problems defined on a bi-dimensional spatial domain. The adaptation is carried out by merging in the numerical scheme the a-priori known informations about the problem, especially those concerning the qualitative behavior of the exact solution and the structure of the system itself. The problem is spatially discretizated through a non-polynomially fitted method of lines, while the time discretization of the resulting system of ODEs (whose vector field consists in both stiff and non-stiff terms) is performed via an implicit-explicit (IMEX) method. The coefficients of the obtained scheme depend on unknown parameters, which need to be properly estimated. In this paper, we propose an estimation strategy based on manipulating the leading term of the local truncation error, whose analytical expression