2 papers
math.NA2025
Discrete Poincaré inequalities: a review on proofs, equivalent formulations, and behavior of constants
Alexandre Ern, Johnny Guzmán, Pratyush Potu +1
We investigate discrete Poincaré inequalities on piecewise polynomial subspaces of the Sobolev spaces H(curl) and H(div) in three space dimensions. We characterize the dependence…
math.NA2025
Local L2-bounded commuting projections using discrete local problems on Alfeld splits
Alexandre Ern, Johnny Guzman, Pratyush Potu +1
We construct projections onto the classical finite element spaces based on Lagrange, Nédélec, Raviart-Thomas, and discontinuous elements on shape-regular simplicial meshes. Our p…