---
res:
  bibo_abstract:
  - "In backward error analysis, an approximate solution to an equation is compared
    to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential
    equations, the two agree up to any power of the step size. If the differential
    equation has a geometric property then the modified equation may share it. In
    this way, known properties of differential equations can be applied to the approximation.
    But for partial differential equations, the known modified equations are of higher
    order, limiting applicability of the theory. Therefore, we study symmetric solutions
    of discretized\r\npartial differential equations that arise from a discrete variational
    principle. These symmetric solutions obey infinite-dimensional functional equations.
    We show that these equations admit second-order modified equations which are Hamiltonian
    and also possess first-order Lagrangians in modified coordinates. The modified
    equation and its associated structures are computed explicitly for the case of
    rotating travelling waves in the nonlinear wave equation.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Robert I
      foaf_name: McLachlan, Robert I
      foaf_surname: McLachlan
  - foaf_Person:
      foaf_givenName: Christian
      foaf_name: Offen, Christian
      foaf_surname: Offen
      foaf_workInfoHomepage: http://www.librecat.org/personId=85279
    orcid: https://orcid.org/0000-0002-5940-8057
  bibo_doi: 10.3934/jgm.2022014
  bibo_issue: '3'
  bibo_volume: 14
  dct_date: 2022^xs_gYear
  dct_language: eng
  dct_publisher: AIMS@
  dct_title: Backward error analysis for variational discretisations of partial  differential
    equations@
...