Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized multiscale finite element method for a strain-limiting
  nonlinear elasticity model   In this paper, we consider multiscale methods for nonlinear elasticity. In
particular, we investigate the Generalized Multiscale Finite Element Method
(GMsFEM) for a strain-limiting elasticity problem. Being a special case of the
naturally implicit constitutive theory of nonlinear elasticity, strain-limiting
relation has presented an interesting class of material bodies, for which
strains remain bounded (even infinitesimal) while stresses can become
arbitrarily large. The nonlinearity and material heterogeneities can create
multiscale features in the solution, and multiscale methods are therefore
necessary. To handle the resulting nonlinear monotone quasilinear elliptic
equation, we use linearization based on the Picard iteration. We consider two
types of basis functions, offline and online basis functions, following the
general framework of GMsFEM. The offline basis functions depend nonlinearly on
the solution. Thus, we design an indicator function and we will recompute the
offline basis functions when the indicator function predicts that the material
property has significant change during the iterations. On the other hand, we
will use the residual based online basis functions to reduce the error
substantially when updating basis functions is necessary. Our numerical results
show that the above combination of offline and online basis functions is able
to give accurate solutions with only a few basis functions per each coarse
region and updating basis functions in selected iterations.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol