Complexes from complexes

DN Arnold, K Hu - Foundations of Computational Mathematics, 2021‏ - Springer
This paper is concerned with the derivation and properties of differential complexes arising
from a variety of problems in differential equations, with applications in continuum …

[HTML][HTML] An asymptotic-preserving and exactly mass-conservative semi-implicit scheme for weakly compressible flows based on compatible finite elements

E Zampa, M Dumbser - Journal of Computational Physics, 2025‏ - Elsevier
We present a novel asymptotic-preserving semi-implicit finite element method for weakly
compressible and incompressible flows based on compatible finite element spaces. The …

A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation

N Ahmed, GR Barrenechea, E Burman, J Guzmán… - SIAM Journal on …, 2021‏ - SIAM
Discretization of Navier--Stokes equations using pressure-robust finite element methods is
considered for the high Reynolds number regime. To counter oscillations due to dominating …

-conforming HDG methods for the stress-velocity formulation of the Stokes equations and the Navier–Stokes equations

W Qiu, L Zhao - Numerische Mathematik, 2024‏ - Springer
In this paper we devise and analyze a pressure-robust and superconvergent HDG method in
stress-velocity formulation for the Stokes equations and the Navier–Stokes equations with …

[HTML][HTML] High-order projection-based upwind method for implicit large eddy simulation

PL Lederer, X Mooslechner, J Schöberl - Journal of Computational Physics, 2023‏ - Elsevier
We assess the ability of three different approaches based on high-order discontinuous
Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass …

Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model

J Kraus, PL Lederer, M Lymbery, J Schöberl - Computer Methods in …, 2021‏ - Elsevier
We consider the quasi-static Biot's consolidation model in a three-field formulation with the
three unknown physical quantities of interest being the displacement u of the solid matrix …

Verification and validation of cylinder drag: Pressure and stress approximations on curved boundaries

IG Gjerde, LR Scott - arxiv preprint arxiv:2306.12362, 2023‏ - arxiv.org
We study a technique for verification of stress and pressure computations on boundaries in
flow simulations. We utilize existing experiments to provide validation of the simulations. We …

A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators

PL Lederer, S Rhebergen - SIAM Journal on Numerical Analysis, 2020‏ - SIAM
The embedded discontinuous Galerkin (EDG) finite element method for the Stokes problem
results in a pointwise divergence-free approximate velocity on cells. However, the …

Formulae and transformations for simplicial tensorial finite elements via polytopal templates

A Sky, M Neunteufel, JS Hale, A Zilian - arxiv preprint arxiv:2405.10402, 2024‏ - arxiv.org
We introduce a unified method for constructing the basis functions of a wide variety of
partially continuous tensor-valued finite elements on simplices using polytopal templates …

The stabilization-free HDG method for fluid-structure interaction in a unified mixed formulation on Alfeld splits

E Chung, L Zhao - Mathematics of Computation, 2024‏ - ams.org
In this paper we propose and analyze a stabilization-free hybridizable discontinuous
Galerkin (HDG) method in stress-velocity formulation for fluid-structure interaction based on …