Inf-sup stable discretization of the quasi-static Biot's equations in poroelasticity
C Kreuzer, P Zanotti - arXiv preprint arXiv:2407.02939, 2024 - arxiv.org
We propose a new full discretization of the Biot's equations in poroelasticity. The
construction is driven by the inf-sup theory, which we recently developed. It builds upon the …
construction is driven by the inf-sup theory, which we recently developed. It builds upon the …
Stability and Monotonicity for Some Discretizations of the Biot's Model
We consider finite element discretizations of the Biot's consolidation model in poroelasticity
with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete …
with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete …
Stability and monotonicity in the low order discretizations of the Biot's model
We consider a finite element discretizations of the Biot's model in poroelasticity with lowest
order (MINI and stabilized P1-P1) elements. We show convergence of discrete schemes …
order (MINI and stabilized P1-P1) elements. We show convergence of discrete schemes …
Stability and monotonicity for some discretizations of the Biot's consolidation model
We consider finite element discretizations of the Biot's consolidation model in poroelasticity
with MINI and stabilized P1–P1 elements. We analyze the convergence of the fully discrete …
with MINI and stabilized P1–P1 elements. We analyze the convergence of the fully discrete …
New stabilized discretizations for poroelasticity and the Stokes' equations
In this work, we consider the popular P1–RT0–P0 discretization of the three-field formulation
of Biot's consolidation problem. Since this finite-element formulation is not uniformly stable …
of Biot's consolidation problem. Since this finite-element formulation is not uniformly stable …
Oscillation-free numerical schemes for Biot's model and their iterative coupling solution
In this work, we present a new stabilization method aimed at removing spurious oscillations
in the pressure approximation of Biot's model for poroelasticity with low permeabilities …
in the pressure approximation of Biot's model for poroelasticity with low permeabilities …
Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability
B Burtschell, P Moireau, D Chapelle - Acta Mathematicae Applicatae …, 2019 - Springer
We consider a previously proposed general nonlinear poromechanical formulation, and we
derive a linearized version of this model. For this linearized model, we obtain an existence …
derive a linearized version of this model. For this linearized model, we obtain an existence …
Robust three-field finite element methods for Biot's consolidation model in poroelasticity
JJ Lee - BIT Numerical Mathematics, 2018 - Springer
We propose a new finite element method for a three-field formulation of Biot's consolidation
model in poroelasticity and prove the a priori error estimates. Uniform-in-time error estimates …
model in poroelasticity and prove the a priori error estimates. Uniform-in-time error estimates …
Guaranteed locking-free finite element methods for Biot's consolidation model in poroelasticity
JJ Lee - arXiv preprint arXiv:1403.7038, 2014 - arxiv.org
We propose a new finite element method for the three-field formulation of Biot's
consolidation model in poroelasticity and prove a priori error estimates. Uniform-in-time error …
consolidation model in poroelasticity and prove a priori error estimates. Uniform-in-time error …
On the optimization of the fixed‐stress splitting for Biot's equations
In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for
poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for …
poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for …