A three-dimensional finite-element method is used to investigate thermal convection in the earth's mantle. The equations of motion are solved implicitly by means of a fast multigrid technique. The computational mesh for the spherical problem is derived from the regular icosahedron. The calculation described use a mesh with 43,554 nodes and 81,920 elements and were run on a Cray X. The earth's mantle is modeled as a thick spherical shell with isothermal, free-slip boundaries. The infinite Prandtl number problem is formulated in terms of pressure, density, absolute temperature, and velocity and assumes an isotropic Newtonian rheology. Solutions are obtained for Rayleigh numbers up to approximately 10/sup 6/ for a variety of modes of heating. Cases initialized with a temperature distribution with warmer temperatures beneath speading ridges and cooler temperatures beneath present subduction zones yield whole-mantle convection solutions with surface velocities that correlate well with currently observed plate velocities. 8 references, 6 figures
