3D consistent boundary‐flux problem in domains with complex geometry
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 19 June 2007
Abstract
Purpose
To obtain error estimates for 3D consistent boundary‐flux approximations.
Design/methodology/approach
Isoparametric approach is used for constructing finite‐element approximations.
Findings
This research study presents a convergence analysis of 3D boundary‐flux approximations. Error estimates are proved for the approximate solutions of the problem under consideration.
Research limitations/implications
General results for a consistent boundary‐flux problem are obtained for all 3D domains with Lipschitz‐continuous boundary. This investigation will be continued studying combined effect of curved boundaries and isoparametric numerical integration. An optimal refined strategy with respect to algorithmic aspects for solving 3D boundary‐flux problem also will be considered.
Practical implications
The obtained results enable engineers to calculate the flux across the curved boundaries using finite element method (FEM).
Originality/value
The paper presents an isoparametric finite‐element method for a 3D consistent boundary‐flux problem in domains with complex geometry. The work is addressed to the possible‐related fields of interest of postgraduate students and specialists in fluid mechanics and numerical analysis.
Keywords
Citation
Todorov, T.D. (2007), "3D consistent boundary‐flux problem in domains with complex geometry", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 5, pp. 522-532. https://doi.org/10.1108/09615530710752982
Publisher
:Emerald Group Publishing Limited
Copyright © 2007, Emerald Group Publishing Limited