Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems (original) (raw)
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In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot's consolidation model of poroelasticity. We approximate the flow variables by a mixed finiteelement space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.
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Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity
IMA Journal of Numerical Analysis, 2020
This work is dedicated to the memory of John W. Barrett, who introduced the concept of inf–sup stability to the corresponding author in the bar at the MAFELAP conference in 1981. We analyze a posteriori error estimators for locking-free mixed finite element approximation of Biot’s consolidation model. Three estimators are described. The simplest of these is a conventional residual-based estimator. We establish bounds relating the estimated and true errors, and show that these are independent of the physical parameters. The other two estimators require the solution of local problems. These local problem estimators are also shown to be reliable, efficient and robust. Numerical results are presented that validate the theoretical estimates, and illustrate the effectiveness of the estimators in guiding adaptive solution algorithms. The IFISS and T-IFISS software packages used for the computational experiments are available online.
A Fully-Conservative Finite Volume Formulation for Coupled Poro- Elastic Problems
2018
Solid mechanics is a research field that deals with the mechanical behavior of a wide variety of materials undergoing external loads. Among the various types of solids, porous materials, for instance, can be found in applications such as soil and rock mechanics, biomechanics, ceramics, etc. These applications are studied in the field of poromechanics, which is a specific branch of the solid mechanics that considers all types of porous materials. An important characteristic of such materials is that they contain a network of interconnected pore channels saturated with a fluid. In most situations the mechanical behavior of the porous matrix and the fluid flow through the pore channels are two tightly coupled phenomena interfering with each other. When the fluid moves from one region to another in the porous matrix it changes the pressure field inside the pore channels, which is perceived by the porous matrix as a force imbalance. As a consequence, the porous matrix tends to deform in ...