Volume 55, pp. 310-340, 2022.

A space-time isogeometric method for the partial differential-algebraic system of Biot's poroelasticity model

Jeremias Arf and Bernd Simeon


Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric space-time methods to this more advanced framework of a partial differential-algebraic equation (PDAE). A space-time approach based on finite elements has already been introduced. We present a new weak formulation in space and time that is appropriate for an isogeometric discretization and analyze its convergence properties. Our approach is based on a single variational problem and hence differs from the iterative space-time schemes considered so far. Further, it enables high-order convergence. Numerical experiments that have been carried out confirm the theoretical findings.

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Key words

Biot's poroelasticity model, isogeometric analysis, space-time discretization, high-order convergence

AMS subject classifications

76S05, 74F10, 65M12, 65M22, 65M60, 65D07

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