Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive discontinuous Galerkin methods on surfaces   We present a dual weighted residual-based a posteriori error estimate for a
discontinuous Galerkin (DG) approximation of a linear second-order elliptic
problem on compact smooth connected and oriented surfaces in $\mathbb{R}^{3}$
which are implicitly represented as level sets of a smooth function. We show
that the error in the energy norm may be split into a "residual part" and a
higher order "geometric part". Upper and lower bounds for the resulting a
posteriori error estimator are proven and we consider a number of challenging
test problems to demonstrate the reliability and efficiency of the estimator.
We also present a novel "geometric" driven refinement strategy for PDEs on
surfaces which considerably improves the performance of the method on complex
surfaces.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex