3 papers
math.NA2025
Computable Poincaré--Friedrichs constants for the de~Rham complex over convex domains and domains with shellable triangulations
Théophile Chaumont-Frelet, Martin Werner Licht, Martin Vohralík
We construct potentials for the exterior derivative, in particular, for the gradient, the curl, and the divergence operators, over domains with shellable triangulations. Notably, t…
math.NA2025
A posteriori error estimates and adaptivity for locally conservative methods. Inexpensive implementation and evaluation, polytopal meshes, iterative linearization and algebraic solvers, and applications to complex porous media flows
Martin Vohralík, Soleiman Yousef
A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology bas…
math.NA2024
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…