  We focus on the finite element method computations with higher-order C1
continuity basis functions that preserve the partition of unity. We show that
the rows of the system of linear equations can be combined, and the test
functions can be sum up to 1 using the partition of unity property at the
quadrature points. Thus, the test functions in higher continuity IGA can be set
to piece-wise constants. This formulation is equivalent to testing with
piece-wise constant basis functions, with supports span over some parts of the
domain. The resulting method is a Petrov-Galerkin formulation with piece-wise
constant test functions. This observation has the following consequences. The
numerical integration cost can be reduced because we do not need to evaluate
the test functions since they are equal to 1. This observation is valid for any
basis functions preserving the partition of unity property. It is independent
of the problem dimension and geometry of the computational domain. It also can
be used in time-dependent problems, e.g., in the explicit dynamics
computations, where we can reduce the cost of generation of the right-hand
side. This summation of test functions can be performed for an arbitrary linear
differential operator resulting from the Galerkin method applied to a PDE where
we discretize with C1 continuity basis functions. The resulting method is
equivalent to a linear combination of the collocations at points and with
weights resulting from applied quadrature over the spans defined by supports of
the piece-wise constant test functions.
