5 papers
Bounded, Commuting, Discrete-trace Preserving Projections
Alexandre Ern, Johnny Guzmán, Pratyush Potu
We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if th…
Discrete Poincare and Bogovskii operators on cochains and Whitney forms
Johnny Guzmán, Anil N. Hirani, Bingyan Liu +1
Smooth Poincare operators are a tool used to show the vanishing of smooth de Rham cohomology on contractible manifolds and have found use in the analysis of finite element methods…
A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms
Johnny Guzmán, Pratyush Potu
We provide a framework for interpreting Discrete Exterior Calculus (DEC) numerical schemes in terms of Finite Element Exterior Calculus (FEEC). We demonstrate the equivalence of co…
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 pro…
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 o…