Isoparametric finite element approximation for a boundary flux problem

Abstract

Purpose

To study and to analyze a second order finite‐element boundary‐flux approximation using isoparametric numerical integration.

Design/methodology/approach

The numerical finite‐element integration is the main method used in this research. Since a domain with curved boundary is considered we apply an isoparametric approach. The lumped flux formulation is another method of approach in this paper.

Findings

This research study presents a careful analysis of the combined effect of the numerical integration and isoparametric FEM on the boundary‐flux error. Some L₂‐norm estimates are proved for the approximate solutions of the problem under consideration.

Research limitations/implications

The authors offer a general study within the framework of the boundary‐flux approximation theory, which completes the results of published works in this scientific field of research.

Practical implications

A useful application is to employ appropriate quadrature formulae without violating the precision of the boundary‐flux FEM. The lumped mass approximation is also an important practical approach to the problem in question.

Originality/value

The paper presents an entire investigation in FE boundary‐flux approximation theory, in particular, elements of arbitrary degree and domains with curved boundaries. The work is addressed to the possible related fields of interest of postgraduate students and specialists in fluid mechanics and numerical analysis.

Citation

Andreev, A.B. and Todorov, T.D. (2006), "Isoparametric finite element approximation for a boundary flux problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 1, pp. 46-66. https://doi.org/10.1108/09615530610636955