The finite element analysis of engineering systems governed by a non-linear quasi-harmonic equation

Abstract It is well known that many engineering situations are governed by a quasi-harmonic equation containing coefficients, which are dependent on the unknown variable or its derivatives, resulting in a non-linear problem for which an iterative scheme of solution is essential. A unified treatment of such problems is undertaken and two solution algorithms are presented. The first is based on a simple interation technique whilst the second follows a generalised Newton-Raphson process. The methods are then applied to non-linear problems in heat conduction, diffusion, magnetostatics and Bingham fluid flow.