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 journalArticlepeer-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 languageEnglish
Article number8
JournalJournal of Scientific Computing
Volume100
Issue number1
Early online date21 May 2024
DOIs
Publication statusE-pub ahead of print - 21 May 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

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