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We investigate the temporal accuracy of two generalized-$\alpha$ schemes for the incompressible Navier-Stokes equations. The conventional approach treats the pressure with the backward Euler method while discretizing the remainder of the…

Numerical Analysis · Mathematics 2020-09-28 Ju Liu , Ingrid S. Lan , Oguz Z. Tikenogullari , Alison L. Marsden

This paper addresses the numerical solution of the two-dimensional Navier--Stokes (NS) equations with nonsmooth initial data in the $L^2$ space, which is the critical space for the two-dimensional NS equations to be well-posed. In this…

Numerical Analysis · Mathematics 2025-10-02 Buyang Li , Qiqi Rao , Hui Zhang , Zhi Zhou

The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity…

Numerical Analysis · Mathematics 2023-07-12 Thierry Gallouët , Raphaèle Herbin , Jean-Claude Latché , David Maltese

In this article, we analyze a two-level finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse…

Numerical Analysis · Mathematics 2021-07-09 Deepjyoti Goswami , Pedro D. Damázio

We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…

Numerical Analysis · Mathematics 2025-04-16 Santolo Leveque , Michele Benzi , Patrick E. Farrell

This manuscript introduces an advanced numerical approach for the integration of incompressible Navier-Stokes (NS) equations using a Time Series Expansion (TSE) method within a Finite Element Method (FEM) framework. The technique is…

Numerical Analysis · Mathematics 2025-05-05 Ahmad Deeb , Denys Dutykh

This paper is concerned with temporal convergence analysis of the recently introduced Dynamically Regularized Lagrange Multiplier (DRLM) method for the incompressible Navier-Stokes equations. A key feature of the DRLM approach is the…

Numerical Analysis · Mathematics 2025-08-20 Cao-Kha Doan , Thi-Thao-Phuong Hoang , Lili Ju , Rihui Lan

This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…

Numerical Analysis · Mathematics 2021-03-17 Walter Boscheri , Lorenzo Pareschi

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product…

Fluid Dynamics · Physics 2016-04-12 Mamdouh S. Mohamed , Anil N. Hirani , Ravi Samtaney

We study convergence of a mixed finite element-finite volume scheme for the compressible Navier Stokes equations in the isentropic regime under the full range of the adiabatic coefficient gamma for the problem with general non zero…

Numerical Analysis · Mathematics 2020-05-05 Young-Sam Kwon , Antonin Novotny

We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…

Numerical Analysis · Mathematics 2022-06-22 Mathias Anselmann , Markus Bause

The error estimates and convergence rate of a two-level MacCormack rapid solver method for solving a two-dimensional incompressible Navier-Stokes equations are analyzed. This represents a continuation of the work on the stability analysis…

Numerical Analysis · Mathematics 2019-03-27 Eric Ngondiep

The Navier-Stokes-Maxwell-Stefan system describes the dynamics of an incompressible gaseous mixture in isothermal condition. In this paper we set up an artificial compressibility type approximation. In particular we focus on the existence…

Analysis of PDEs · Mathematics 2018-05-18 Michele Dolce , Donatella Donatelli

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

Numerical Analysis · Mathematics 2020-08-28 Sana Keita , Abdelaziz Beljadid , Yves Bourgault

We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…

Numerical Analysis · Mathematics 2017-12-27 Hadrien Montanelli , Yuji Nakatsukasa

The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…

Computational Physics · Physics 2018-01-11 Oscar Bruno , Max Cubillos

This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…

Numerical Analysis · Mathematics 2020-10-01 Heiko Gimperlein , Ceyhun Oezdemir , David Stark , Ernst P. Stephan

In this paper, a third-order time adaptive algorithm with less computation, low complexity is provided for shale reservoir model based on coupled fluid flow with porous media flow. The algorithm combines the three-step linear time filters…

Numerical Analysis · Mathematics 2024-07-26 Jian Li , Lele Chen , Yi Qin , Zhangxin Chen

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…

Numerical Analysis · Mathematics 2018-09-10 Gurpreet Singh , Mary F. Wheeler