We have developed a Bound Preserving Discontinuous Galerkin advection method for modeling the advection diffusion equation that governs the temperature in computational models of convection in the Earth's mantle. This new algorithm prevents overshoot in the temperature at the tips of subducting slabs, which heretofore have lead to very large errors in the viscosity at the slab tip, due to the fact that the viscosity has a steep gradient near the slab tip and the viscosity depends exponentially on the temperature. We are now using this new algorithm to model subducting slabs.




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