A review on the recent advances of the flow and transport phenomena in tight and shale
formations is presented in this work. Exploration of oil and gas in resources that were once …

We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …

This paper is concerned with the numerical simulation of time-dependent variably-saturated
Darcian flow problems described by the Richards equation. We present the adaptive higher …

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 …

This paper presents a methodology for computing upper and lower bounds for both the
algebraic and total errors in the context of the conforming finite element discretization of the …

In this paper we derive an a posteriori error estimate for the numerical approximation of the
solution of a system modeling the flow of two incompressible and immiscible fluids in a …

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 …

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 …

In this paper we derive a posteriori error estimates for the compositional model of multiphase
Darcy flow in porous media, consisting of a system of strongly coupled nonlinear unsteady …