Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Filtered Stochastic Galerkin Methods For Hyperbolic Equations   Uncertainty Quantification for nonlinear hyperbolic problems becomes a
challenging task in the vicinity of shocks. Standard intrusive methods lead to
oscillatory solutions and can result in non-hyperbolic moment systems. The
intrusive polynomial moment (IPM) method guarantees hyperbolicity but comes at
higher numerical costs. In this paper, we filter the gPC coefficients of the
Stochastic Galerkin (SG) approximation, which allows a numerically cheap
reduction of oscillations. The derived filter is based on Lasso regression
which sets small gPC coefficients of high order to zero. We adaptively choose
the filter strength to obtain a zero-valued highest order moment, which allows
optimality of the corresponding optimization problem. The filtered SG method is
tested for Burgers' and the Euler equations. Results show a reduction of
oscillations at shocks, which leads to an improved approximation of expectation
values and the variance compared to SG and IPM.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph