Space-time isogeometric method for a nonlocal parabolic problem

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 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.