A centered coupling scheme for lattice Boltzmann methods solves Biot's poroelasticity model stably for strong coupling and captures discontinuous solutions in consolidation problems.
Diffusion in poro-elastic media
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Proves unique strong global solutions for small data in a 3D viscoelastic Navier-Stokes-Biot system with Beavers-Joseph-Saffman conditions via spectral analysis, and establishes a Serrin-type blow-up criterion.
A conformal finite element and implicit Euler discretization is proposed and analyzed for the Biot-contact variational problem, proving existence, uniqueness, stability, and a priori error estimates, with numerical verification of the rates.
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Strong well-posedness of a fluid--poro-viscoelastic interaction problem: An approach by Spectral analysis
Proves unique strong global solutions for small data in a 3D viscoelastic Navier-Stokes-Biot system with Beavers-Joseph-Saffman conditions via spectral analysis, and establishes a Serrin-type blow-up criterion.
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Numerical analysis of the Biot equations coupled to frictional contact mechanics
A conformal finite element and implicit Euler discretization is proposed and analyzed for the Biot-contact variational problem, proving existence, uniqueness, stability, and a priori error estimates, with numerical verification of the rates.