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 …

We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …

In this paper we develop an a posteriori error analysis for an augmented mixed-primal finite
element approximation of a stationary viscous flow and transport problem. The governing …

This paper is concerned with the analysis of coupled mixed finite element methods applied
to the Biot's consolidation model. We consider two mixed formulations that use the stress …

We present novel H (div) and H 1 liftings of given piecewise polynomials over a hierarchy of
simplicial meshes, based on a global solve on the coarsest mesh and on local solves on …

We consider two-phase flow in a porous medium composed of two different rock types, so
that the capillary pressure field is discontinuous at the interface between the rocks. This is a …

We develop in this work an adaptive inexact smoothing Newton method for a nonconforming
discretization of a variational inequality. As a model problem, we consider the contact …

This paper develops an a posteriori error estimate for lowest-order locally conservative
methods on meshes consisting of general polytopal elements. We focus on the ease of …

We derive equilibrated reconstructions of the Darcy velocity and of the total stress tensor for
Biot's poro-elasticity problem. Both reconstructions are obtained from mixed finite element …

In this paper, we present a simple a posteriori error estimate for the weak Galerkin finite
element method for the Stokes equation. This residual type estimator can be applied to …