3 papers
math.NA2026
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…
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
Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method
Erik Burman, Rebecca Durst, Miguel A. Fernández +2
We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [J. Numer. Math., 31(1):59--77, 2023] for a parabolic-parabolic interface problem…