A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation
Year: 2026
Type: preprint
Abstract: We study a time fractional convection-diffusion-reaction equation in a bounded domain $Ω\subset\mathbb{R}^2$. A stabilized numerical scheme satisfying a discrete maximum principle is constructed by combining the conforming linear finite element method with the algebraic flux correction method. The resulting semi-discrete scheme is nonlinear, and its well-posedness is established. Assuming nonsmooth initial data, we derive error estimates for the semi-discrete scheme using energy arguments. For the temporal discretization, we employ the L1 method, obtaining a fully discrete scheme for which we prove well-posedness and the discrete maximum principle. We also present numerical experiments that validate the order of convergence as well as we test our schemes to solutions that possess layers.
Source: arXiv (Cornell University)
Author: Pervolianakis, Christos
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208767391