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Time-continuous strongly conservative space–time finite element methods for the dynamic Biot model

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  • Kraus, Johannes
  • Lymbery, Maria
  • Osthues, Kevin

Abstract

We consider the dynamic Biot model (see Biot, 1962) describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a saturated porous medium. This model couples a hyperbolic equation for momentum balance to a second-order in time dynamic Darcy law and a parabolic equation for the balance of mass and is here considered in three-field formulation with the displacement of the elastic matrix, the fluid velocity, and the fluid pressure being the physical fields of interest.

Suggested Citation

  • Kraus, Johannes & Lymbery, Maria & Osthues, Kevin, 2026. "Time-continuous strongly conservative space–time finite element methods for the dynamic Biot model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 250(C), pages 813-828.
    • Handle: RePEc:eee:matcom:v:250:y:2026:i:c:p:813-828
    DOI: 10.1016/j.matcom.2026.07.017
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