Computational techniques for kinematically constrained convection models

In order to unify plate kinematics with mantle dynamics we need to be able to apply plate-like boundary conditions to convection models in which the penalty for the model failing to satisfy the condition can be weighted according to the uncertainty in the kinematic reconstruction. Constraints typically include "rigidity" of oceanic plate interiors and prescribed plate motion vectors. An additional requirement is a kinematically-plausible dynamic model for the deformation at plate boundaries and regions where there is poor observational constraints on the kinematics. Numerically, the application of the rigidity constraint can be achieved by either penalizing the strain-rate in the plate interior or by prescribing that the velocities must be consistent with a rigid body motion. Plate reconstruction information is imposed upon the rigid plates by an additional penalty on the mismatch between the convection model plate velocities and those from the reconstructed plate motions. Here we first formulate the numerical techniques required to apply arbitrary and coupled constraints on mantle convection and to solve the resulting systems of equations efficiently. We then explore the effectiveness of each of these approaches.