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This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

Numerical Analysis · Mathematics 2019-02-01 Victor DeCaria , William Layton , Haiyun Zhao

We consider the motion of incompressible viscous non-homogeneous fluid described by the Navier-Stokes equations in a bounded cylinder under boundary slip conditions. Assume that the third co-ordinate axis is the axis of the cylinder.…

Analysis of PDEs · Mathematics 2012-02-07 Wojciech M. Zajaczkowski

We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to…

Analysis of PDEs · Mathematics 2015-11-26 Timo Heister , Maxim A. Olshanskii , Leo G. Rebholz

We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…

Numerical Analysis · Mathematics 2026-04-23 Carolyn M. V. Pethrick , Siva Nadarajah

A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…

Numerical Analysis · Mathematics 2016-07-12 Shuqin Wang , Jinyun Yuan , Weihua Deng , Yujiang Wu

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that…

Numerical Analysis · Mathematics 2023-08-31 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…

Analysis of PDEs · Mathematics 2016-01-19 Jacek Cyranka , Piotr B Mucha , Edriss S Titi , Piotr Zgliczyński

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…

Fluid Dynamics · Physics 2022-07-13 James Gabbard , Thomas Gillis , Philippe Chatelain , Wim M. van Rees

We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…

Numerical Analysis · Mathematics 2025-10-22 L. Beirão da Veiga , F. Dassi , S. Gómez

We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…

Numerical Analysis · Mathematics 2016-10-06 Herbert Egger

We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…

Analysis of PDEs · Mathematics 2026-01-22 Jos\é Francisco Rodrigues , Lisa Santos

In the present contribution we propose a novel conforming Finite Element scheme for the time-dependent Navier-Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a…

Numerical Analysis · Mathematics 2024-04-23 L. Beirão da Veiga , F. Dassi , G. Vacca

We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in…

Numerical Analysis · Mathematics 2023-02-22 Jens Visbech , Allan P. Engsig-Karup , Harry B. Bingham

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…

Numerical Analysis · Mathematics 2025-04-02 Jialin Xie , Xiaodi Zhang

The numerical implementation of finite element discretization method for the stream function formulation of a linearized Navier-Stokes equations is considered. Algorithm 1 is applied using Argyris element. Three global orderings of nodes…

Numerical Analysis · Mathematics 2025-10-20 F. Fairag , N. Almulla

Split form schemes for Euler and Navier-Stokes equations are useful for computation of turbulent flows due to their better robustness. This is because they satisfy additional conservation properties of the governing equations like kinetic…

Numerical Analysis · Mathematics 2021-05-03 Vikram Singh , Praveen Chandrashekar

We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity…

Numerical Analysis · Mathematics 2018-10-17 J. Shipton , T. H. Gibson , C. J. Cotter

The following work presents a generalized (extended) finite element formulation for the advection-diffusion equation. Using enrichment functions that represent the exponential nature of the exact solution, smooth numerical solutions are…

Numerical Analysis · Computer Science 2008-06-25 D. Z. Turner , K. B. Nakshatrala , K. D. Hjelmstad

We consider the dynamic Biot model (see [Biot, M. A. J. Appl. Phys. 33, 1482--1498 (1962)]) describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a…

Numerical Analysis · Mathematics 2025-07-29 Johannes Kraus , Maria Lymbery , Kevin Osthues

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

Optimization and Control · Mathematics 2013-08-09 Tuğba Akman , Bülent Karasözen