84 citations · 140 across the 12 of their papers we have counts for
13 papers
POD-ROM methods: from a finite set of snapshots to continuous-in-time approximations
Bosco Garcia-Archilla, Volker John, Julia Novo
This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis i…
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…
Optimal bounds for POD approximations of infinite horizon control problems based on time derivatives
Javier de Frutos, Bosco Garcia-Archilla, Julia Novo
In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton-Jacobi-…
POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution: Error bounds for the pressure
Bosco García-Archilla, Volker John, Sarah Katz +1
Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the…
Robust error bounds for the Navier-Stokes equations using implicit-explicit second order BDF method with variable steps
Bosco Garcia-Archilla, Julia Novo
This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration tw…
Error analysis of proper orthogonal decomposition data assimilation schemes for the Navier-Stokes equations
Bosco García Archilla, Julia Novo, Samuele Rubino
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added t…
Uniform in time error estimates for a finite element method applied to a downscaling data assimilation algorithm for the Navier-Stokes equations
García-Archilla, Julia Novo, Edriss S. Titi
In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two and three dimensional Na…
Error analysis of projection methods for non inf-sup stable mixed finite elements. The transient Stokes problem
Javier de Frutos, Bosco García-Archilla, Julia Novo
A modified Chorin-Teman (Euler non-incremental) projection method and a modified Euler incremental projection method for non inf-sup stable mixed finite elements are analyzed. The…
Error analysis of projection methods for non inf-sup stable mixed finite elements. The Navier-Stokes equations
Javier de Frutos, Bosco García-Archilla, Julia Novo
We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations.…
Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements
Javier de Frutos, Bosco García-Archilla, Volker John +1
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case…
Static two-grid mixed finite-element approximations to the Navier-Stokes equations
Javier de Frutos, Bosco García-Archilla, Julia Novo
A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finit…
Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
Javier de Frutos, Bosco García-Archilla, Julia Novo
We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied ov…
A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations
Javier de Frutos, Bosco García-Archilla, Julia Novo
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier…