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A space-time isogeometric method for the partial differential-algebraic system of Biot’s poroelasticity model. (English) Zbl 1490.76202

Summary: 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.

MSC:

76S05 Flows in porous media; filtration; seepage
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65D07 Numerical computation using splines

Software:

Matlab; GeoPDEs
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Full Text: DOI arXiv

References:

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