Space-Time Isogeometric Method for a Nonlocal Parabolic Problem
Numerical Analysis
2026-01-27 v3 Numerical Analysis
Abstract
In the present work, we focus on the space-time isogeometric discretization of a parabolic problem with a nonlocal diffusion coefficient. The existence and uniqueness of the solution for the continuous space-time variational formulation are proven. We prove the existence of the discrete solution and also establish the a priori error estimate for the space-time isogeometric scheme. The non-linear system is linearized through Picards method and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, results of some numerical experiments are presented.
Keywords
Cite
@article{arxiv.2408.00450,
title = {Space-Time Isogeometric Method for a Nonlocal Parabolic Problem},
author = {Sudhakar Chaudhary and Shreya Chauhan and Monica Montardini},
journal= {arXiv preprint arXiv:2408.00450},
year = {2026}
}
Comments
This work has been accepted for publication in the journal Advances in Computational Mathematics on 26th January 2026