This paper introduces a newly developed wavelet technique for modeling
of geophysical flow processes in multiple dimensions. The method
utilizes the idea of collocation with the multilevel wavelet
approximation. The multilevel structure of the algorithm facilitates the
computational adaptation of the grid refinement in regions where sharp
variations occur. We hat-e tested this algorithm for viscoelastic flows
with viscosity contrasts up to 10(12). We have confirmed the findings of
stress amplification in the thin highly viscous layer. The new method
allows us to conduct the calculations for thin layers and high viscosity
contrasts, close enough for realistic mantle-lithospheric interaction.
Our results demonstrate the potential usefulness of the wavelet
technique in large-scale numerical simulations in the geosciences.