Comparison between two methods of modelling the flow in a mantle with laterally variable viscosity

Summary Two different spectral methods have recently been used to model the flow driven by harmonic loads in a Newtonian mantle with laterally variable viscosity. The first method, by Zhang and Christensen (1993), transforms the problem with a general three-dimensional viscosity into a series of standard spherically symmetric problems. A different approach has been chosen by Martinec et al. (1993). Their method is based on integral formulation of the problem. The solution, which corresponds to a minimum of the dissipative energy, is found by means of the gradient search. We have tested the efficiency and numerical behaviour of both methods. The results of our tests favour the former method which is found more accurate and significantly faster than the gradient algorithm.