In this paper, we provide a priori and a posteriori error analyses of an augmented mixed finite element method with Lagrange multipliers applied to elliptic equations in divergence form with mixed boundary conditions. The ...

Residual type a posteriori error estimators are introduced in this paper for an advection–diffusion–reaction problem with a Dirac delta source term. The error is measured in an adequately weighted W1,pW1,p-norm. These ...

This paper deals with a posteriori error estimates for advection–reaction–diffusion equations. In particular, error estimators based on the solution of local problems are derived for a stabilized finite element method. ...

We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In ...

This work proposes and analyses an adaptive finite element scheme for the fully non-linear incompressible Navier-Stokes equations. A residual a posteriori error estimator is shown to be effective and reliable with respect ...

In this paper we develop an a posteriori error analysis for an augmented discontinuous Garlerkin formulation applied to the Darcy flow. More precisely, we derive a reliable and efficient a posteriori error estimator, ...

We consider the Oseen problem with nonhomogeneous Dirichlet boundary conditions on a part of the boundary and a Neumann type boundary condition on the remaining part. Suitable least squares terms that arise from the ...

We consider an augmented mixed finite element method for incompressible fluid flows and develop a simple a posteriori error analysis. We obtain an a posteriori error estimator that is reliable and locally efficient. We ...

This article is concerned with the Stokes system with nonhomogeneous source terms and nonhomogeneous Dirichlet boundary condition. First, we reformulate the problem in its dual mixed form, and then, we study its corresponding ...

We consider a stabilized mixed finite element method introduced recently for the generalized Stokes problem. The method is obtained by adding suitable least squares terms to the dual-mixed variational formulation of the ...