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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.…
Projection-Based Reconstruction for Achieving High-Order Accuracy from Low-Order DGSEM Simulations
Xukun Wang, Suyash Shrestha, Oscar A. Marino +1
High-order discontinuous Galerkin spectral element methods (DGSEM) based on Legendre-Gauss-Lobatto (LGL) nodes provide accurate and efficient discretizations for conservation laws.…
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…
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…