Pre-Publicación 2026-22
Abraham J. Arenas, Juan Barajas-Calonge, Gilberto González-Parra, Luis M. Villada:
Convergence analysis of a nonstandard finite volume method for a diffusion-production-destruction model
Abstract:
In this paper, we introduce and analyze a nonstandard finite volume (NSFV) scheme for a diffusion–production–destruction model. The numerical method is formulated by coupling an unconditionally stable nonstandard time discretization, which is dynamically consistent with the associated system of ordinary differential equations, with an implicit finite-volume discretization of the diffusion operator on triangular meshes. We establish the existence of a discrete solution to the NSFV scheme and, through non-negativity, $L^2$-estimates and compactness arguments, we prove the convergence of the scheme to an admissible weak solution of the model. We further develop a second-order extension in both space and time that preserves the positivity of the solutions. Finally, numerical experiments over two-dimensional spatial domains with complex geometries are presented to illustrate the behavior of the model and to assess the performance of the NSFV scheme.
