arXiv subjects

Shreya Chauhan

Publications and source records attributed to Shreya Chauhan.

2 recordsLinked to original sources

arXiv2026

Space-Time Isogeometric Method for a Nonlocal Parabolic Problem

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.

math.NA↗

arXiv2025

Space-time isogeometric method for a linear fourth order time dependent problem

This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the system is discretized by employing the tensor product spline spaces of time and spatial variables. We use the Babuska's theorem to prove the well-posedness of the continuous variational formulation. Also, the inf-sup stability condition at discrete level is established, which we use to prove the error estimates for the proposed method. Finally, to demonstrate the convergence of the scheme, few numerical results are reported.

math.NA↗