This article presents a computable and efficient procedure for a posteriori error estimations
of approximate solutions of Darcy's flows given by a Multiscale Hybrid Mixed method. Based …

We derive a unified framework for goal-oriented a posteriori estimation covering in particular
higher-order conforming, nonconforming, and discontinuous Galerkin finite element …

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 derive an anisotropic a posteriori error estimate for the adaptive conforming virtual
element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we …

In this paper, we present a posteriori error estimate of weak Galerkin (WG) finite element
methods based on the second order elliptic interface problems. This estimate can be applied …

In this article, we consider the time-dependent convection-diffusion-reaction equation
coupled with the Darcy equation. We propose a numerical scheme based on finite element …

In this paper we review the hypercircle method of Prager and Synge. This theory inspired
several studies and induced an active research in the area of a posteriori error analysis. In …

We present an a posteriori error analysis for the mixed virtual element method (mixed VEM)
applied to second order elliptic equations in divergence form with mixed boundary …

This work focuses on the development of adaptive timesteps, stopping criteria, and error
control strategies for reservoir simulations with fully implicit (FIM) solvers. Using a rigorous …

In this work we develop an a posteriori-based adaptive local multilevel mesh refinement
strategy for the Darcy porous media flow problem discretized with the finite volume method …