A global residual‐based stabilization for equal‐order finite element approximations of incompressible flows

Abstract Due to simplicity in implementation and data structure, elements with equal‐order interpolation of velocity pressure are very popular finite‐element‐based flow simulations. Although such pairs inf‐sup unstable, various stabilization techniques exist circumvent that yield accurate approximations. The most one is the pressure‐stabilized Petrov–Galerkin (PSPG) method, which consists relaxing incompressibility constraint a weighted residual momentum equation. Yet, PSPG can perform poorly for low‐order diffusion‐dominated flows, since first‐order polynomial spaces unable approximate second‐order derivatives required evaluating viscous part term. Alternative normally require additional projections or unconventional structures. In this context, we present novel technique rewrites term as boundary term, thereby allowing complete computation even lowest‐order elements. Our method has similar structure standard residual‐based formulations, but computed globally instead only element interiors. This results scheme does not relax incompressibility, leading improved new simple implement wide range parameters, confirmed by numerical examples.