Flow and transport in tight and shale formations: A review
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 …
formations is presented in this work. Exploration of oil and gas in resources that were once …
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs
A Ern, M Vohralík - SIAM Journal on Scientific Computing, 2013 - SIAM
We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …
nonlinear partial differential equations of diffusion type. To solve these systems, some …
An introductory review on a posteriori error estimation in finite element computations
L Chamoin, F Legoll - SIAM Review, 2023 - SIAM
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 …
problems solved with the finite element method. For the sake of simplicity and clarity, we …
[HTML][HTML] Adaptive higher-order space-time discontinuous Galerkin method for the computer simulation of variably-saturated porous media flows
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 …
Darcian flow problems described by the Richards equation. We present the adaptive higher …
[HTML][HTML] Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics …
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 …
coupled poromechanics problems. We particularly consider the space–time formulation of …
Estimating and localizing the algebraic and total numerical errors using flux reconstructions
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 …
algebraic and total errors in the context of the conforming finite element discretization of the …
An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow
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 …
solution of a system modeling the flow of two incompressible and immiscible fluids in a …
A posteriori error analysis for a viscous flow-transport problem
M Alvarez, GN Gatica, R Ruiz-Baier - … : Mathematical Modelling and …, 2016 - esaim-m2an.org
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 …
element approximation of a stationary viscous flow and transport problem. The governing …
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation
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 …
simplicial meshes, based on a global solve on the coarsest mesh and on local solves on …
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
DA Di Pietro, E Flauraud, M Vohralík… - Journal of Computational …, 2014 - Elsevier
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 …
Darcy flow in porous media, consisting of a system of strongly coupled nonlinear unsteady …