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

TL;DR

This paper develops a novel isogeometric space-time method for Biot's poroelasticity equations, formulating a unified variational approach that achieves high-order convergence and is validated through numerical experiments.

Contribution

It introduces a new weak formulation for Biot's equations suitable for isogeometric discretization, enabling a single variational problem and high-order convergence.

Findings

The method achieves high-order convergence in numerical tests.

The approach is based on a unified variational formulation.

Numerical experiments confirm theoretical convergence rates.

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.