---
_id: '63676'
abstract:
- lang: eng
text: "\r\n Purpose\r\n The
purpose of this paper is to develop new methods of error representation to improve
the accuracy and numerical efficiency of a posteriori and goal-oriented adaptive
framework of elastoplasticity with Prandtl–Reuss type material laws.\r\n
\ \r\n \r\n Design/methodology/approach\r\n
\ To obtain new methods of error representation for
a posteriori and goal-oriented error estimators, weak forms of primal and dual
problems are investigated starting with the initial boundary value problem (IBVP).
Then, we approximate both problems using temporal discretization. Additionally,
we introduce a secant form considering the nonlinearity of elasto-plastic constitutive
equations, which is approximated by a tangent form. Finally, we obtain numerical
primal and dual solutions and their corresponding error approximations of discretized
primal and dual problems, allowing to build several goal-oriented a posteriori
error estimators on temporal and spatial adaptive refinement by inserting primal
solutions, dual solutions and their error approximations as arguments in residuals
of both weak forms as well as in the secant form of the bilinear residual.\r\n
\ \r\n \r\n Findings\r\n
\ An elasto-plastic material is investigated in a framework
of goal-oriented error estimator by using separately several methods of error
representation to deal with either temporal or spatial adaptive refinement, as
well as with both refinements leading to an effective reduction of computational
effort. Specifically, new error representations based on goal-oriented error estimators
are presented and obtained from primal and dual residuals, which use only primal
solutions or only dual solutions or a combination of primal and dual solutions
as arguments. Error representations obtained from primal residuals and evaluated
using only primal arguments do not require the formulation of a dual problem.\r\n
\ \r\n \r\n Research
limitations/implications\r\n The effectiveness
of the different proposed methods is illustrated by an example of a perforated
sheet for adaptive spatial refinement where new mesh adaptation methods of error
representation are compared against existing mesh adaptation methods such as uniform
mesh refinement, mesh refinement based on gradient indicators and adjoint-based
methods in literature. The framework generates a balanced mesh consisting of fine,
medium and coarse elements for accurate results, avoiding a numerically costly
simulation with only fine elements.\r\n \r\n
\ \r\n Originality/value\r\n
\ All new proposed methods of error representation successfully
estimate actual errors during mesh adaptivity. Furthermore, the proposed methods
of error representation allow us to obtain significant reduction and equidistribution
of spatial error at the end of the mesh adaptivity process. Their application
to a framework of goal-oriented error estimation due to time and mesh adaptivity
remains an open issue.\r\n "
author:
- first_name: Arnold
full_name: Tchomgue Simeu, Arnold
id: '83075'
last_name: Tchomgue Simeu
- first_name: Ismail
full_name: Caylak, Ismail
id: '75'
last_name: Caylak
- first_name: Richard
full_name: Ostwald, Richard
id: '106876'
last_name: Ostwald
orcid: 0000-0003-2147-8444
citation:
ama: Tchomgue Simeu A, Caylak I, Ostwald R. Error representations for goal-oriented
a posteriori error estimation in elasto-plasticity
with applications to mesh adaptivity. Engineering Computations. Published
online 2026:1-40. doi:10.1108/ec-12-2023-0975
apa: Tchomgue Simeu, A., Caylak, I., & Ostwald, R. (2026). Error representations
for goal-oriented a posteriori error
estimation in elasto-plasticity with applications to mesh adaptivity. Engineering
Computations, 1–40. https://doi.org/10.1108/ec-12-2023-0975
bibtex: '@article{Tchomgue Simeu_Caylak_Ostwald_2026, title={Error representations
for goal-oriented a posteriori error
estimation in elasto-plasticity with applications to mesh adaptivity}, DOI={10.1108/ec-12-2023-0975}, journal={Engineering
Computations}, publisher={Emerald}, author={Tchomgue Simeu, Arnold and Caylak,
Ismail and Ostwald, Richard}, year={2026}, pages={1–40} }'
chicago: Tchomgue Simeu, Arnold, Ismail Caylak, and Richard Ostwald. “Error Representations
for Goal-Oriented a Posteriori Error
Estimation in Elasto-Plasticity with Applications to Mesh Adaptivity.” Engineering
Computations, 2026, 1–40. https://doi.org/10.1108/ec-12-2023-0975.
ieee: 'A. Tchomgue Simeu, I. Caylak, and R. Ostwald, “Error representations for
goal-oriented a posteriori error
estimation in elasto-plasticity with applications to mesh adaptivity,” Engineering
Computations, pp. 1–40, 2026, doi: 10.1108/ec-12-2023-0975.'
mla: Tchomgue Simeu, Arnold, et al. “Error Representations for Goal-Oriented
a Posteriori Error Estimation in Elasto-Plasticity
with Applications to Mesh Adaptivity.” Engineering Computations, Emerald,
2026, pp. 1–40, doi:10.1108/ec-12-2023-0975.
short: A. Tchomgue Simeu, I. Caylak, R. Ostwald, Engineering Computations (2026)
1–40.
date_created: 2026-01-21T06:49:18Z
date_updated: 2026-01-21T06:50:58Z
department:
- _id: '9'
- _id: '952'
- _id: '321'
doi: 10.1108/ec-12-2023-0975
language:
- iso: eng
page: 1-40
publication: Engineering Computations
publication_identifier:
issn:
- 0264-4401
- 1758-7077
publication_status: published
publisher: Emerald
quality_controlled: '1'
status: public
title: Error representations for goal-oriented a posteriori error
estimation in elasto-plasticity with applications to mesh adaptivity
type: journal_article
user_id: '85414'
year: '2026'
...