Zobrazeno 1 - 10
of 397
pro vyhledávání: '"Rebholz, Leo"'
This paper considers continuous data assimilation (CDA) in partial differential equation (PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove that long-time optimally accurate solutions are obtained for such paramet
Externí odkaz:
http://arxiv.org/abs/2408.00396
Autor:
Olshanskii, Maxim A., Rebholz, Leo G.
This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations. Additionally, it enhan
Externí odkaz:
http://arxiv.org/abs/2405.03796
We analyze and test a simple-to-implement two-step iteration for the incompressible Navier-Stokes equations that consists of first applying the Picard iteration and then applying the Newton iteration to the Picard output. We prove that this compositi
Externí odkaz:
http://arxiv.org/abs/2402.12304
The purpose of this paper is to develop a practical strategy to accelerate Newton's method in the vicinity of singular points. We present an adaptive safeguarding scheme with a tunable parameter, which we call adaptive gamma-safeguarding, that one ca
Externí odkaz:
http://arxiv.org/abs/2402.09295
We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is incorporated/assimilated i
Externí odkaz:
http://arxiv.org/abs/2401.06749
Autor:
Olshanskii, Maxim A., Rebholz, Leo G.
Publikováno v:
Computer Methods in Applied Mechanics and Engineering 418 (2024): 116583
We consider local balances of momentum and angular momentum for the incompressible Navier-Stokes equations. First, we formulate new weak forms of the physical balances (conservation laws) of these quantities, and prove they are equivalent to the usua
Externí odkaz:
http://arxiv.org/abs/2309.05585
This paper considers improving the Picard and Newton iterative solvers for the Navier-Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data assimilatio
Externí odkaz:
http://arxiv.org/abs/2306.01172
We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modelin
Externí odkaz:
http://arxiv.org/abs/2302.05962
Autor:
Pollock, Sara, Rebholz, Leo G.
This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteration of Anderson acceleration. The filtering strategy consists of two ste
Externí odkaz:
http://arxiv.org/abs/2211.12953
We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular that the Gron
Externí odkaz:
http://arxiv.org/abs/2205.05160