Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new anisotropic mesh adaptation method based upon hierarchical a
  posteriori error estimates   A new anisotropic mesh adaptation strategy for finite element solution of
elliptic differential equations is presented. It generates anisotropic adaptive
meshes as quasi-uniform ones in some metric space, with the metric tensor being
computed based on hierarchical a posteriori error estimates. A global
hierarchical error estimate is employed in this study to obtain reliable
directional information of the solution. Instead of solving the global error
problem exactly, which is costly in general, we solve it iteratively using the
symmetric Gauss--Seidel (GS) method. Numerical results show that a few GS
iterations are sufficient for obtaining a reasonably good approximation to the
error for use in anisotropic mesh adaptation. The new method is compared with
several strategies using local error estimators or recovered Hessians.
Numerical results are presented for a selection of test examples and a
mathematical model for heat conduction in a thermal battery with large
orthotropic jumps in the material coefficients.

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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ