Guaranteed locking-free finite element methods for Biot's consolidation\n model in poroelasticity

2014/03/27 by Jeonghun J. Lee, Lee, Jeonghun J.
Engineering · Mathematics · #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1403.7038

openalex publication_date 2014/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new finite element method for the three-field formulation of\nBiot's consolidation model in poroelasticity and prove a priori error\nestimates. Uniform-in-time error estimates of all the unknowns are obtained for\nboth semidiscrete solutions and fully discrete solutions with the backward\nEuler time discretization. The novelty of our method is that the error analysis\ndoes not require the assumption that the constrained specific storage\ncoefficient is uniformly positive. Therefore the method is guaranteed to be\nlocking-free without the additional assumption on material parameters.\n

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