Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fully adaptive multilevel stochastic collocation strategy for solving
  elliptic PDEs with random data   We propose and analyse a fully adaptive strategy for solving elliptic PDEs
with random data in this work. A hierarchical sequence of adaptive mesh
refinements for the spatial approximation is combined with adaptive anisotropic
sparse Smolyak grids in the stochastic space in such a way as to minimize the
computational cost. The novel aspect of our strategy is that the hierarchy of
spatial approximations is sample dependent so that the computational effort at
each collocation point can be optimised individually. We outline a rigorous
analysis for the convergence and computational complexity of the adaptive
multilevel algorithm and we provide optimal choices for error tolerances at
each level. Two numerical examples demonstrate the reliability of the error
control and the significant decrease in the complexity that arises when
compared to single level algorithms and multilevel algorithms that employ
adaptivity solely in the spatial discretisation or in the collocation
procedure.

15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat