Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditioning of Finite Element Equations with Arbitrary Anisotropic
  Meshes   Bounds are developed for the condition number of the linear finite element
equations of an anisotropic diffusion problem with arbitrary meshes. They
depend on three factors. The first, factor proportional to a power of the
number of mesh elements, represents the condition number of the linear finite
element equations for the Laplacian operator on a uniform mesh. The other two
factors arise from the mesh nonuniformity viewed in the Euclidean metric and in
the metric defined by the diffusion matrix. The new bounds reveal that the
conditioning of the finite element equations with adaptive anisotropic meshes
is much better than what is commonly feared. Diagonal scaling for the linear
system and its effects on the conditioning are also studied. It is shown that
the Jacobi preconditioning, which is an optimal diagonal scaling for a
symmetric positive definite sparse matrix, can eliminate the effects of mesh
nonuniformity viewed in the Euclidean metric and reduce those effects of the
mesh viewed in the metric defined by the diffusion matrix. Tight bounds on the
extreme eigenvalues of the stiffness and mass matrices are obtained. Numerical
examples are given.

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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: nucl-th