相关论文: Design of convergence criterion for fixed stress s…

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…

We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also referred to as MPET models. The focus of the paper is on the…

Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable.…

The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…

In this paper we develop adaptive iterative coupling schemes for the Biot system modeling coupled poromechanics problems. We particularly consider the space-time formulation of the fixed-stress iterative scheme, in which we first solve the…

An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…

In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are…

Voids can be observed at various scales in ductile materials, frequently of sizes lower than the grain size, leading to porous single crystals materials. Two local deformation modes of porous ductile (single crystals) materials have been…

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…

In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…

In this work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial…

In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the…

This work presents several new results concerning the analysis of the convergence of binary, univariate, and linear subdivision schemes, all related to the {\it contractivity factor} of a convergent scheme. First, we prove that a convergent…

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

The quasistatic rate-independent damage combined with linearized plasticity with hardening at small strains is investigated. The fractional-step time discretisation is devised with the purpose to obtain a numerically efficient scheme…

In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [Comput.…

The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…

This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…