The temporal behavior of projection methods for viscous
incompressible flows is analyzed and numerically assessed. The methods
considered result from algebraically splitting the linear system
corresponding to each time step, in such a way that the computation of
velocity is segregated from that of pressure. Each method is characterized
by two (possibly equal) approximate inverses (\mathsf{B}1 and \mathsf{B}2)
of the momentum-equation velocity matrix, plus a parameter γ which renders
the method non-incremental (if γ=0) or incremental (ifγ=1). The classical
first-order projection method, together with more sophisticated methods
(Perot's second-order method, Yosida method, pseudo-exact factorization
method) and their incremental variants are put into the same algebraic form
and their accuracy numerically tested. Splitting errors of first, second
and third order in the time step size δ t are obtained, depending on the
method.