  In this note we will explore some applications of the recently constructed
piecewise affine, $H^1$-conforming element that fits in a discrete de Rham
complex [Christiansen and Hu, Generalized finite element systems for smooth
differential forms and Stokes' problem. Numer. Math. 140 (2018)]. In particular
we show how the element leads to locking free methods for incompressible
elasticity and viscosity robust methods for the Brinkman model.
