Using lower order elements for the temperature/compositional discretization

The default settings of ASPECT use quadratic finite elements for the velocity. Given that the temperature and compositional fields essentially (up to material parameters) satisfy advection equations of the kind \(\partial_t T + \mathbf u \cdot \nabla T = \ldots\), it seems appropriate to also use quadratic finite element shape functions for the temperature and compositional fields.

However, this is not mandatory. If you do not care about high accuracy in these fields and are mostly interested in the velocity or pressure field, you can select lower-order finite elements in the input file. The polynomial degrees are controlled with the parameters in the discretization section of the input file, see Discretization, in particular by Temperature polynomial degree and Composition polynomial degree.

As with the other parameters discussed above and below, it is worthwhile comparing the results you get with different values of these parameters when making a decision whether you want to save on accuracy in order to reduce compute time. An example of how this choice affects the accuracy you get is discussed in Convection in a 2d box.