This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a f...

In this paper, we deal with the numerical approximation of some porous-thermoelastic problems. Since inertial effects are assumed to be negligible, resulting motion equations quasistatic. Then, by using finite element method and implicit Euler scheme, a fully discrete is introduced. We prove stability property main error estimates result, from which conclude linear convergence under appropriate...

This article studies the least-squares finite element method for the linearized, stationary Navier–Stokes equation based on the stress-velocity-pressure formulation in d dimensions (d = 2 or 3). The least-squares functional is simply defined as the sum of the squares of the L2 norm of the residuals. It is shown that the homogeneous least-squares functional is elliptic and continuous in the H(di...

Error analysis is defined by the following concern: bounding the output variation of a (nonlinear) function with respect to a given variation of the input variables. This paper investigates this issue in the framework of interval analysis. The classical way of analyzing the error is to linearize the function around the point corresponding to the actual input, but this method is local and not re...

Error analysis is defined by the following concern: Bounding the output variation of a (nonlinear) function with respect to a given variation of the input variables. This paper investigates this issue in the framework of interval analysis. The classical way of analyzing the error is to linearize the function around the point corresponding to the actual input, but this method is local and not re...