79 citations · 295 across the 22 of their papers we have counts for
5 papers · 1 filter
Higher-order compatible discretization on hexahedrals
Jasper Kreeft, Marc Gerritsma
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constr…
A Geometric Approach Towards Momentum Conservation
D. Toshniwal, R. H. M. Huijsmans, M. I. Gerritsma
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we tre…
Mimetic Spectral Element advection
Artur Palha, Pedro Pinto Rebelo, Marc Gerritsma
We present a discretization of the linear advection of differential forms on bounded domains. The framework previously established is extended to incorporate the Lie derivative, $\…
Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
Artur Palha, Pedro Pinto Rebelo, René Hiemstra +2
This paper introduces the basic concepts for physics-compatible discretization techniques. The paper gives a clear distinction between vectors and forms. Based on the difference be…
Mixed Mimetic Spectral Element method applied to Darcy's problem
Pedro Pinto Rebelo, Artur Palha, Marc Gerritsma
We present a discretization for Darcy's problem using the recently developed Mimetic Spectral Element Method. The gist lies in the exact discrete representation of integral relatio…