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

TL;DR

This paper develops a space-time isogeometric method for solving a linear fourth order time-dependent problem, utilizing tensor product spline spaces and rigorous stability and error analysis.

Contribution

It introduces a novel space-time isogeometric approach for fourth order problems, including stability proofs and error estimates, with numerical validation.

Findings

The method is well-posed and stable.

Error estimates are established for the discretization.

Numerical results confirm convergence and accuracy.

Abstract

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.