Mesh-Dependent L2-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions

Konstantinos Chrysafinos; Emmanuil H. Georgoulis; Vassilis D. Papadopoulos

doi:10.1007/s10915-024-02559-5

Mesh-Dependent L²-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions

Konstantinos Chrysafinos, Emmanuil H. Georgoulis^*, Vassilis D. Papadopoulos

^*Corresponding author for this work

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

Abstract

This work is concerned with the proof of L²-like norm residual-type a posteriori error estimates for finite element methods for elliptic problems with non-essential boundary conditions, such as Neumann or Robin type. To ensure the proof of lower bounds (efficiency), a non-standard mesh-dependent L²-like norm is used for the error. The proof of lower bounds requires a carefully constructed C¹-conforming ’bubble’-function. A series of numerical experiments is presented, showcasing the good performance of the estimators.

Original language	English
Article number	8
Journal	Journal of Scientific Computing
Volume	100
Issue number	1
Early online date	21 May 2024
DOIs	https://doi.org/10.1007/s10915-024-02559-5
Publication status	Published - Jul 2024

Keywords

A posteriori error analysis
Finite element methods
Non-essential boundary conditions
Residual-type estimators
Robin boundary conditions

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1007/s10915-024-02559-5

Cite this

@article{beea75ae7df54c069f7de5cda0b62a36,

title = "Mesh-Dependent L2-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions",

abstract = "This work is concerned with the proof of L2-like norm residual-type a posteriori error estimates for finite element methods for elliptic problems with non-essential boundary conditions, such as Neumann or Robin type. To ensure the proof of lower bounds (efficiency), a non-standard mesh-dependent L2-like norm is used for the error. The proof of lower bounds requires a carefully constructed C1-conforming {\textquoteright}bubble{\textquoteright}-function. A series of numerical experiments is presented, showcasing the good performance of the estimators.",

keywords = "A posteriori error analysis, Finite element methods, Non-essential boundary conditions, Residual-type estimators, Robin boundary conditions",

author = "Konstantinos Chrysafinos and Georgoulis, {Emmanuil H.} and Papadopoulos, {Vassilis D.}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

year = "2024",

month = jul,

doi = "10.1007/s10915-024-02559-5",

language = "English",

volume = "100",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - Mesh-Dependent L2-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions

AU - Chrysafinos, Konstantinos

AU - Georgoulis, Emmanuil H.

AU - Papadopoulos, Vassilis D.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024/7

Y1 - 2024/7

N2 - This work is concerned with the proof of L2-like norm residual-type a posteriori error estimates for finite element methods for elliptic problems with non-essential boundary conditions, such as Neumann or Robin type. To ensure the proof of lower bounds (efficiency), a non-standard mesh-dependent L2-like norm is used for the error. The proof of lower bounds requires a carefully constructed C1-conforming ’bubble’-function. A series of numerical experiments is presented, showcasing the good performance of the estimators.

AB - This work is concerned with the proof of L2-like norm residual-type a posteriori error estimates for finite element methods for elliptic problems with non-essential boundary conditions, such as Neumann or Robin type. To ensure the proof of lower bounds (efficiency), a non-standard mesh-dependent L2-like norm is used for the error. The proof of lower bounds requires a carefully constructed C1-conforming ’bubble’-function. A series of numerical experiments is presented, showcasing the good performance of the estimators.

KW - A posteriori error analysis

KW - Finite element methods

KW - Non-essential boundary conditions

KW - Residual-type estimators

KW - Robin boundary conditions

UR - http://www.scopus.com/inward/record.url?scp=85193570822&partnerID=8YFLogxK

U2 - 10.1007/s10915-024-02559-5

DO - 10.1007/s10915-024-02559-5

M3 - Article

AN - SCOPUS:85193570822

SN - 0885-7474

VL - 100

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 1

M1 - 8

ER -

Mesh-Dependent L²-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Embargoed Document

Fingerprint

Cite this