A C1C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions

In 1988, Worsey and Piper constructed a trivariate macro-element based on C1C1 quadratic splines defined over a split of a tetrahedron into 24 subtetrahedra. However, this local element can only be used to construct a corresponding macro-element spline space over tetrahedral partitions that satisfy some very restrictive geometric constraints. We show that by further refining their split, it is possible to construct a macro-element also based on C1C1 quadratic splines that can be used with arbitrary tetrahedral partitions. The resulting macro-element space is stable and provides full approximation power.