Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity

Ehsan Rabizadeh; Amir Saboor Bagherzadeh; Timon Rabczuk

doi:10.1016/j.compstruc.2016.05.024

Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity

Ehsan Rabizadeh^*, Amir Saboor Bagherzadeh, Timon Rabczuk

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We present an adaptive method for dynamic coupled thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark method. Different recovery methods such as superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR) and weighted superconvergent patch recovery (WSPR) are used to estimate the error in the quantity of interest (QoI). By using adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed on the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.

Original language	English
Pages (from-to)	187-211
Number of pages	25
Journal	Computers and Structures
Volume	173
DOIs	https://doi.org/10.1016/j.compstruc.2016.05.024
Publication status	Published - 2016 Sept 1

Bibliographical note

Funding Information:
The first author would like gratefully acknowledge for the financial support of this work which was provided by the Deutscher Akademischer Austauschdienst (DAAD).

Publisher Copyright:
© 2016 Elsevier Ltd

Keywords

Adaptive mesh refinement
Classical coupled thermoelasticity
Dynamic thermoelastic problem
Error in the quantity of interest
Finite element method
Goal-oriented error estimation

ASJC Scopus subject areas

Civil and Structural Engineering
Modelling and Simulation
General Materials Science
Mechanical Engineering
Computer Science Applications

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10.1016/j.compstruc.2016.05.024

Cite this

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title = "Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity",

abstract = "We present an adaptive method for dynamic coupled thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark method. Different recovery methods such as superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR) and weighted superconvergent patch recovery (WSPR) are used to estimate the error in the quantity of interest (QoI). By using adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed on the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.",

keywords = "Adaptive mesh refinement, Classical coupled thermoelasticity, Dynamic thermoelastic problem, Error in the quantity of interest, Finite element method, Goal-oriented error estimation",

author = "Ehsan Rabizadeh and \{Saboor Bagherzadeh\}, Amir and Timon Rabczuk",

note = "Funding Information: The first author would like gratefully acknowledge for the financial support of this work which was provided by the Deutscher Akademischer Austauschdienst (DAAD). Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd",

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doi = "10.1016/j.compstruc.2016.05.024",

language = "English",

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T1 - Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity

AU - Rabizadeh, Ehsan

AU - Saboor Bagherzadeh, Amir

AU - Rabczuk, Timon

N1 - Funding Information: The first author would like gratefully acknowledge for the financial support of this work which was provided by the Deutscher Akademischer Austauschdienst (DAAD). Publisher Copyright: © 2016 Elsevier Ltd

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We present an adaptive method for dynamic coupled thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark method. Different recovery methods such as superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR) and weighted superconvergent patch recovery (WSPR) are used to estimate the error in the quantity of interest (QoI). By using adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed on the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.

AB - We present an adaptive method for dynamic coupled thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark method. Different recovery methods such as superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR) and weighted superconvergent patch recovery (WSPR) are used to estimate the error in the quantity of interest (QoI). By using adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed on the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.

KW - Adaptive mesh refinement

KW - Classical coupled thermoelasticity

KW - Dynamic thermoelastic problem

KW - Error in the quantity of interest

KW - Finite element method

KW - Goal-oriented error estimation

UR - https://www.scopus.com/pages/publications/84978160550

U2 - 10.1016/j.compstruc.2016.05.024

DO - 10.1016/j.compstruc.2016.05.024

M3 - Article

AN - SCOPUS:84978160550

SN - 0045-7949

VL - 173

SP - 187

EP - 211

JO - Computers and Structures

JF - Computers and Structures

ER -

Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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