Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of mixed FEMs for non-selfadjoint indefinite second-order
  linear elliptic PDEs   For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE
with general coefficients $\mathbf A, \mathbf b,\gamma$ in $L^\infty$ and
symmetric and uniformly positive definite coefficient matrix $\mathbf A$, this
paper proves that mixed finite element problems are uniquely solvable and the
discrete solutions are uniformly bounded, whenever the underlying shape-regular
triangulation is sufficiently fine. This applies to the Raviart-Thomas (RT) and
Brezzi-Douglas-Marini (BDM) finite element families of any order and in any
space dimension and leads to the best-approximation estimate in $H(div)\times
L^2$ as well as in in $L^2\times L^2$ up to oscillations. This generalises
earlier contributions for piecewise Lipschitz continuous coefficients to
$L^\infty$ coefficients. The compactness argument of Schatz and Wang for the
displacement-oriented problem does not apply immediately to the mixed
formulation in $H(div)\times L^2$. But it allows the uniform approximation of
some $L^2$ contributions and can be combined with a recent $L^2$
best-approximation result from the medius analysis. This technique circumvents
any regularity assumption and the application of a Fortin interpolation
operator.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph