Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearly constrained evolutions of critical points and an application to
  cohesive fractures   We introduce a novel constructive approach to define time evolution of
critical points of an energy functional. Our procedure, which is different from
other more established approaches based on viscosity approximations in infinite
dimension, is prone to efficient and consistent numerical implementations, and
allows for an existence proof under very general assumptions. We consider in
particular rather nonsmooth and nonconvex energy functionals, provided the
domain of the energy is finite dimensional. Nevertheless, in the infinite
dimensional case study of a cohesive fracture model, we prove a consistency
theorem of a discrete-to-continuum limit. We show that a quasistatic evolution
can be indeed recovered as a limit of evolutions of critical points of finite
dimensional discretizations of the energy, constructed according to our scheme.
To illustrate the results, we provide several numerical experiments both in one
and two dimensions. These agree with the crack initiation criterion, which
states that a fracture appears only when the stress overcomes a certain
threshold, depending on the material.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc