Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Goal-oriented a posteriori estimation of numerical errors in the
  solution of multiphysics systems   This paper develops a general methodology for a posteriori error estimation
in time-dependent multiphysics numerical simulations. The methodology builds
upon the generalized-structure additive Runge--Kutta (GARK) approach to time
integration. GARK provides a unified formulation of multimethods that simulate
complex systems by applying different discretization formulas and/or different
time steps to individual components of the system. We derive discrete GARK
adjoints and analyze their time accuracy. Based on the adjoint method, we
establish computable a posteriori identities for the impacts of both temporal
and spatial discretization errors on a given goal function. Numerical examples
with reaction-diffusion systems illustrate the accuracy of the derived error
measures. Local error decompositions are used to illustrate the power of this
framework in adaptive refinements of both temporal and spatial meshes.

16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an