Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions
Provides a general framework for divergence-free finite elements in incompressible flow simulations, addressing a known bottleneck in arbitrary dimensions.
Constructed stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions, achieving divergence-free velocity approximations. The method works for any dimension and polynomial degree.
We construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps the discrete velocity space onto the the discrete pressure space; thus, when applied to models of incompressible flows, the pairs yield divergence-free velocity approximations. The key result is a local inf-sup stability that holds for any dimension and for any polynomial degree. With this result, we construct global divergence-free and stable pairs in arbitrary dimension and for any polynomial degree.