Numerical approaches to solid-state convection in planetary bodies

Numerical methods suitable for the calculation of finite-amplitude thermal convection in planetary interiors are reviewed. Three methods of approach are described and compared; namely, finite-difference, finite-element and spectral procedures. Application of each approach to three-dimensional solid-state convection with complex rheology is examined. Finite-difference methods have enjoyed some success to date. However, future developments are likely to favor finite-element methods when rheology and boundaries are complex, and spectral methods when accuracy is paramount and rheology and boundaries are simple.