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<p>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 Picard’s method, and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, the results of some numerical experiments are presented.</p>

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Space-time isogeometric method for a nonlocal parabolic problem

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月12日

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  • Sudhakar Chaudhary,
  • Shreya Chauhan,
  • Monica Montardini

摘要

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 Picard’s method, and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, the results of some numerical experiments are presented.