On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime

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On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows (2015, methodology): “3, a modification of the test function can be applied for this pair of finite element spaces, see [43].”
A discontinuous skeletal method for the viscosity-dependent Stokes problem (2015, unknown): “— is the variational crime introduced recently in [29, 30] in the lowest-order case with Crouzeix–Raviart/ P 0 mixed ﬁnite elements.”