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arXiv · 2408.00450

Space-Time Isogeometric Method for a Nonlocal Parabolic Problem

Sudhakar Chaudhary·Shreya Chauhan·Monica Montardini
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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.

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Sudhakar Chaudhary, Shreya Chauhan, Monica Montardini. 2024-08-01. Space-Time Isogeometric Method for a Nonlocal Parabolic Problem. https://arxiv.org/abs/2408.00450

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