Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations

DOI10.1007/s10444-020-09806-xzbMath1454.65115arXiv1904.06113OpenAlexW3039621445MaRDI QIDQ2216608

Julia Novo, Bosco García-Archilla

Publication date: 16 December 2020

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.06113

zbMATH Keywords

Navier-Stokes equationsdata assimilationdownscalingmixed finite elements methodsfully discrete schemesuniform-in-time error estimates

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (12)

The bleeps, the sweeps, and the creeps: convergence rates for dynamic observer patterns via data assimilation for the 2D Navier-Stokes equations ⋮ Error analysis of proper orthogonal decomposition data assimilation schemes with grad-div stabilization for the Navier-Stokes equations ⋮ Dynamically learning the parameters of a chaotic system using partial observations ⋮ Simple and efficient continuous data assimilation of evolution equations via algebraic nudging ⋮ Accelerating and enabling convergence of nonlinear solvers for Navier-Stokes equations by continuous data assimilation ⋮ Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation ⋮ Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: the 2D Navier-Stokes equation paradigm ⋮ Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms ^* ⋮ Finite time synchronization of the continuous/discrete data assimilation algorithms for Lorenz 63 system based on the back and forth nudging techniques ⋮ Continuous data assimilation of a discretized barotropic vorticity model of geophysical flow ⋮ A parallel grad-div stabilized finite element algorithm for the Stokes equations with damping ⋮ Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows

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