What discretization method does Sundance use?
The method of discretization is determined by a number of factors: the choice of weak formulation of a problem, the choice of basis functions for each field, the choice of quadrature rules for integration, and by the choice of stabilization scheme (if any) used. For example, the Navier-Stokes equations of incompressible fluid mechanics can be written in either pressure-velocity form or vorticity-streamfunction form, each of which leads to different discretization issues. With the pressure-velocity form, a naive choice of basis functions will likely lead to an unstable scheme; a suitable combination of bases for velocity and pressure must be used, or alternatively, the system can be stabilized by adding certain non-physical terms to the equation set. Sundance allows essentially any choice of weak formulation, and then the choice of basis functions and quadrature rules is limited by the set that has been implemented at this time.
