Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error estimation and adaptivity for stochastic collocation finite
  elements Part II: multilevel approximation   A multilevel adaptive refinement strategy for solving linear elliptic partial
differential equations with random data is recalled in this work. The strategy
extends the a posteriori error estimation framework introduced by Guignard and
Nobile in 2018 (SIAM J. Numer. Anal, 56, 3121--3143) to cover problems with a
nonaffine parametric coefficient dependence. A suboptimal, but nonetheless
reliable and convenient implementation of the strategy involves approximation
of the decoupled PDE problems with a common finite element approximation space.
Computational results obtained using such a single-level strategy are presented
in part I of this work (Bespalov, Silvester and Xu, arXiv:2109.07320). Results
obtained using a potentially more efficient multilevel approximation strategy,
where meshes are individually tailored, are discussed herein. The codes used to
generate the numerical results are available online.

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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci