2024/01/09 by Johannes Kraus, Kraus, Johannes, Maria Lymbery +5
Computer Science · Earth and Planetary Sciences · Engineering · #74H15 65M15 65M60 74F10 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2401.04609
openalex publication_date 2024/01/09 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
We consider the dynamic Biot model 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. The 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. A family of variational space-time finite element methods is proposed that combines a continuous-in-time Galerkin ansatz of arbitrary polynomial degree with inf-sup stable H(\rmdiv)-conforming approximations of discontinuous Galerkin (DG) type in case of the displacement and a mixed approximation of the flux, its time derivative and the pressure field. We prove error estimates in a combined energy norm as well as L2~error estimates in space for the individual fields for both maximum and L2 norm in time which are optimal for the displacement and pressure approximations.