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Space–time isogeometric discretization of linear fourth order time-dependent problem with second-order-in-space formulation
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DOI：10.1016/j.enganabound.2026.106846.png)
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Abstract
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Space–time isogeometric method is widely used for solving many problems involving second order spatial derivatives. In this work, we analyze the space–time isogeometric method for a linear fourth order time-dependent problem. We propose a scheme which is based on a second-order-in-space variational formulation. We discuss the well-posedness of the space–time weak formulation via the Banach–Nec̆as–Babus̆ka’s theorem. The second-order-in-space formulation requires at least C1 regularity in space, and therefore here we consider the high-order spline basis functions in isogeometric analysis, which allows C1 conforming space–time discretization of the fourth order problem. The a priori error estimates are also established for the proposed method. Moreover, an efficient solver is provided to solve the linear system obtained from the space–time isogeometric discretization of the fourth order problem. Finally, some numerical experiments are presented to validate the theoretical findings.
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