Anisotropic adaptive methods based on a metric related to the Hessian of the solution are
considered. We propose a metric targeted to the minimization of interpolation error
gradient for a nonconforming linear finite element approximation of a given piecewise
regular function on a polyhedral domain of
, ≥ 2. We also
present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative
to such a...

We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, a conforming mixed finite element method which takes into account an approximation of the middle line of the arch is given. But for a very small thickness such a method gives poor error bounds. the conforming Galerkin method is then enriched with residual-free bubble functions.

We consider a general loaded arch problem with a small thickness. To
approximate the solution of this problem, a conforming mixed finite element
method which takes into account an approximation of the middle line of the
arch is given. But for a very small thickness such a method gives poor error
bounds. the conforming Galerkin method is then enriched with residual-free
bubble functions.

We present a new method for generating a -dimensional simplicial mesh
that minimizes the
-norm,
> 0, of the interpolation error or its gradient. The method
uses edge-based error estimates to build a tensor metric. We describe and analyze the
basic steps of our method

In this paper, a new a posteriori error estimator for nonconforming convection diffusion
approximation problem, which relies on the small discrete problems solution in stars, has
been established. It is equivalent to the energy error up to data oscillation without any
saturation assumption nor comparison with residual estimator

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