The lithosphere/asthenosphere interaction in subduction zones can be viewed as a fluid/solid coupling problem. Therefore, I have developed a code which couples a standard FE Stokes solver and the FE solid solver ADELI (,). The coupling is performed by the use of a Fictitious Domain Method (see  for a complete description of the algorithm). Below is a simplified description of the strategy :
 Hassani, R., Jongmans, D., & Chéry, J. (1997). Study of plate deformation and stress in subduction processes using two‐dimensional numerical models. Journal of Geophysical Research: Solid Earth (1978–2012), 102(B8), 17951-17965.
 Chéry, J., Zoback, M. D., & Hassani, R. (2001). An integrated mechanical model of the San Andreas fault in central and northern California. Journal of Geophysical Research: Solid Earth (1978–2012), 106(B10), 22051-22066.
 Cerpa, N. G., Hassani, R., Gerbault, M., & Prévost, J. H. (2014). A fictitious domain method for lithosphere‐asthenosphere interaction: Application to periodic slab folding in the upper mantle. Geochemistry, Geophysics, Geosystems, 15(5), 1852-1877.