Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive and anisotropic finite element approximation : Theory and
  algorithms   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. This procedure plays a key role in numerous applications
of scientific computing. The use of anisotropic triangles allows to improve the
efficiency of the procedure by introducing long and thin triangles that fit in
particular the directions of the possible curves of discontinuity.
  Given a norm X of interest and a function f to be approximated, we formulate
the problem of optimal mesh adaptation, as minimizing the approximation error
over all (possibly anisotropic) triangulations of prescribed cardinality. We
address the four following questions related to this problem:
  I. How does the approximation error behave in the asymptotic regime when the
number of triangles N tends to infinity, when f is a smooth function ?
  II. Which classes of functions govern the rate of decay of the approximation
error as N grows, and are in that sense naturally tied to the problem of
optimal mesh adaptation?
  III. Could this optimization problem, which is posed on triangulations of a
given cardinality N, be replaced by an equivalent more tractable problem posed
on a continuous object?
  IV. Is it possible to produce a near-optimal sequence of triangulations using
a hierarchical refinement procedure?

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol