5 papers · 1 filter
An Approximate Bounded Cochain Projection
Marc Gerritsma, Suyash Shrestha
This paper presents a construction of a projector from an infinite-dimensional Hilbert complex of differential -forms onto a finite-dimensional piecewise polynomial sub-complex.…
Optimal solutions employing an algebraic Variational Multiscale approach Part II: Application to Navier-Stokes
Suyash Shrestha, Marc Gerritsma, Gonzalo Rubio +2
This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear proble…
Space-time discretization for barotropic flow stemming from a multisymplectic variational formulation
Mukthesh Mahadev, Marc Gerritsma
This study proposes and analyses a novel higher-order, structure preserving discretization method for inviscid barotropic flows from a Lagrangian perspective. The method is built o…
Optimal solutions employing an algebraic Variational Multiscale approach Part I: Steady Linear Problems
Suyash Shrestha, Marc Gerritsma, Gonzalo Rubio +2
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We intro…
Construction and application of an algebraic dual basis and the Fine-Scale Greens' Function for computing projections and reconstructing unresolved scales
Suyash Shrestha, Joey Dekker, Marc Gerritsma +2
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABIL…