Parameter-Robust Stochastic Galerkin Mixed Approximation for Linear Poroelasticity with Uncertain Inputs

Linear poroelasticity models have important applications in biology and geophysics. In particular, the well-known Biot consolidation model describes coupled interaction between linear response of a porous elastic medium saturated with fluid diffusive flow within it, assuming small deformations. Although deterministic finite element methods for solving them numerically been well studied, there is little work to date on robust algorithms uncertain inputs performing uncertainty quantification (UQ). The has number physical parameters whose precise values are often real world scenarios. this work, we introduce analyze well-posedness new five-field spatially varying Young's modulus hydraulic conductivity field. By working properly weighted norm, establish that weak solution stable respect variations key parameters, including Poisson ratio. We then novel locking-free stochastic Galerkin mixed method nearly incompressible case. Armed an appropriate construct parameter-robust preconditioner associated discrete systems. Our facilitates forward UQ, allowing efficient calculation statistical quantities interest, provably ratio, Biot--Willis constant, storage coefficient, as discretization parameters.