Modeling evolving discontinuities

We present a framework for solving partial differential equations with discontinuities in the solution across evolving surfaces. The partition-of-unity/extended finite element approach is adopted, and it is demonstrated that such methods can be used in combination with a form compiler to generate equation-specific parts of a program. The automated generation of code makes it straightforward to incorporate discontinuities in formulations involving multiple fields, using both Lagrange and non-Lagrange basis functions. The approach is illustrated through some salient code extracts