8 citations · 8 across the 6 of their papers we have counts for
6 papers
Analysis of continuous data assimilation with large (or even infinite) nudging parameters
Amanda Diegel, Xuejian Li, Leo G. Rebholz
This paper considers continuous data assimilation (CDA) in partial differential equation (PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove tha…
Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence
Sara Pollock, Leo Rebholz, Xuemin Tu +1
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 t…
Enhancing nonlinear solvers for the Navier-Stokes equations with continuous (noisy) data assimilation
Bosco Garcia-Archilla, Xuejian Li, Julia Novo +1
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 sol…
Accelerating and enabling convergence of nonlinear solvers for Navier-Stokes equations by continuous data assimilation
Xuejian Li, Elizabeth V. Hawkins, Leo G. Rebholz +1
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…
Removing splitting/modeling error in projection/penalty methods for Navier-Stokes simulations with continuous data assimilation
Elizabeth Hawkins, Leo G. Rebholz, Duygu Vargun
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 c…
Data-Driven Filtered Reduced Order Modeling Of Fluid Flows
X. Xie, M. Mohebujjaman, L. G. Rebholz +1
We propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps: (i) In the…