Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics

Abstract

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.

Cited by in corpus (4)

• Improved rates for a space-time FOSLS of parabolic PDEs
• Error estimates for the Smagorinsky turbulence model: enhanced stability through scale separation and numerical stabilization
• A well-posed First Order System Least Squares formulation of the instationary Stokes equations
• An arbitrary-order fully discrete Stokes complex on general polyhedral meshes