A Posteriori error estimates for Darcy-Forchheimer's problem coupled with the convection-diffusion-reaction equation

In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the variational formulation associated to the problem, and discretize it by using the finite element method. We prove optimal a posteriori errors with two types of calculable error indicators. The first one is linked to the linearization and the second one to the discretization. Then we find upper and lower error bounds under additional regularity assumptions on the exact solutions. Finally, numerical computations are performed to show the effectiveness of the obtained error indicators.Comment: arXiv admin note: text overlap with arXiv:2202.1164

A POSTERIORI ANALYSIS OF AN ITERATIVE ALGORITHM FOR NAVIER-STOKES PROBLEM

This work deals with a posteriori error estimates for the Navier-Stokes equations. We propose a finite element discretization relying on the Galerkin method and we solve the discrete problem using an iterative method. Two sources of error appear, the discretization error and the linearization error. Balancing these two errors is very important to avoid performing an excessive number of iterations. Several numerical tests are provided to evaluate the efficiency of our indicators

Parallel Computing Investigations for the Projection Method Applied to the Interface Transport Scheme of a Two-phase Flow by the Method of Characteristics

This paper deals with the discretization of the problem of mould filling in iron foundry and its numerical solution using a Schwarz domain decomposition method. An adapted technique for domain decomposition methods that suits the discretization in time by the method of characteristics is introduced. Furthermore, the projection method is used to reduce the computation time. Finally, numerical experiments show and validate the effectiveness of the proposed scheme

Astrocyte activation and reactive gliosis : A new target in stroke?

Stroke is an acute insult to the central nervous system (CNS) that triggers a sequence of responses in the acute, subacute as well as later stages, with prominent involvement of astrocytes. Astrocyte activation and reactive gliosis in the acute stage of stroke limit the tissue damage and contribute to the restoration of homeostasis. Astrocytes also control many aspects of neural plasticity that is the basis for functional recovery. Here, we discuss the concept of intermediate filaments (nanofilaments) and the complement system as two handles on the astrocyte responses to injury that both present attractive opportunities for novel treatment strategies modulating astrocyte functions and reactive gliosis.Peer reviewe