3D consistent boundary‐flux problem in domains with complex geometry

Abstract

PurposeTo obtain error estimates for 3D consistent boundary‐flux approximations.Design/methodology/approachIsoparametric approach is used for constructing finite‐element approximations.FindingsThis 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/implicationsGeneral 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 implicationsThe obtained results enable engineers to calculate the flux across the curved boundaries using finite element method (FEM).Originality/valueThe 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.