84 citations · 141 across the 23 of their papers we have counts for
24 papers · 1 filter
Computational study of Proper Orthogonal Decomposition methods for parametric approximations
Bosco García-Archilla, Alicia García-Mascaraque, Julia Novo
This paper studies the computational implementation of proper orthogonal decomposition reduced-order models (POD-ROMs) for evolutionary parametric time-dependent partial differenti…
Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations
Bosco García-Archilla, V. John, Julia Novo
Error bounds for fully discrete schemes for the evolutionary incompressible Navier--Stokes equations are derived in this paper. For the time integration we apply BDF- methods, $…
Pointwise error bounds in POD methods without difference quotients
Bosco García-Archilla, Julia Novo
In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been…
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-…
Second order error bounds for POD-ROM methods based on first order divided differences
Bosco García-Archilla, Volker John, Julia Novo
This note proves, for simplicity for the heat equation, that using BDF2 as time stepping scheme in POD-ROM methods with snapshots based on difference quotients gives both the optim…
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…
Pressure and convection robust bounds for continuous interior penalty divergence-free finite element methods for the incompressible Navier-Stokes equations
Bosco García-Archilla, Julia Novo
In this paper we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an…
POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution
Bosco García-Archilla, Volker John, Julia Novo
In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations…
On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
Bosco García-Archilla, Julia Novo, Samuele Rubino
We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear…
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…
Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
Javier de Frutos, Julia Novo
In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that considering a time disc…
Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows
Julia Novo, Samuele Rubino
Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are considered and analyzed. We consider two cases, the case in which the snapshots are bas…
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…
Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations
Bosco García-Archilla, Julia Novo
In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscali…
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 Non Inf-sup Stable Discretizations of the time-dependent Navier--Stokes Equations with Local Projection Stabilization
Javier de Frutos, Bosco García-Archilla, Volker John +1
This paper studies non inf-sup stable finite element approximations to the evolutionary Navier--Stokes equations. Several local projection stabilization (LPS) methods corresponding…
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…