94 citations · 287 across the 29 of their papers we have counts for
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Adaptive and anisotropic finite element approximation : Theory and algorithms
Jean-Marie Mirebeau
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. Th…
Sharp asymptotics of the Lp approximation error for interpolation on block partitions
Yuliya Babenko, Tatyana Leskevich, Jean-Marie Mirebeau
Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the s…
Adaptive and anisotropic piecewise polynomial approximation
Albert Cohen, Jean-Marie Mirebeau
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is de…
Adaptive multiresolution analysis based on anisotropic triangulations
Albert Cohen, Nira Dyn, Frédéric Hecht +1
A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarch…
Greedy bisection generates optimally adapted triangulations
Jean-Marie Mirebeau, Albert Cohen
We study the properties of a simple greedy algorithm for the generation of data-adapted anisotropic triangulations. Given a function f, the algorithm produces nested triangulations…
Anisotropic smoothness classes : from finite element approximation to image models
Jean-Marie Mirebeau, Albert Cohen
We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of a…
Optimal Meshes for Finite Elements of Arbitrary Order
Jean-Marie Mirebeau
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its in…
The optimal aspect ratio for piecewise quadratic anisotropic finite element approximation
Jean-Marie Mirebeau
Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedu…
Optimally Adapted Meshes for Finite Elements of Arbitrary Order and W1p Norms
Jean-Marie Mirebeau
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its in…
Non conforming vector finite elements for H(curl) intersected with H(div)
Jean-Marie Mirebeau
We present a family of nonconforming vector finite elements of arbitrary order for problems posed on the space (curl) intersected with H(div) on a bidimensional domain. This result…