A space-time isogeometric method for the partial differential-algebraic system of Biot's poroelasticity model
Abstract
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. But we present a new weak formulation in space and time that is appropriate for an isogeometric discretization and analyze the 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.
Keywords
Cite
@article{arxiv.2102.07798,
title = {A space-time isogeometric method for the partial differential-algebraic system of Biot's poroelasticity model},
author = {Jeremias Arf and Bernd Simeon},
journal= {arXiv preprint arXiv:2102.07798},
year = {2021}
}