A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation
Abstract
We study a time fractional convection-diffusion-reaction equation in a bounded domain Ω⊂ℝ2. 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.
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BibTeX
@misc{pervolianakis2026stabilized,
title = {{A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation}},
author = {Christos Pervolianakis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03808},
eprint = {2609.03808},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03808},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation
AU - Christos Pervolianakis
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03808
UR - https://arxiv.org/abs/2609.03808
AB - We study a time fractional convection-diffusion-reaction equation in a bounded domain Ω⊂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.
ER -