scholarly journals Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations

2020 ◽  
Vol 58 (1) ◽  
pp. 410-429
Author(s):  
Bosco García-Archilla ◽  
Julia Novo ◽  
Edriss S. Titi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Data Assimilation ◽  
Error Estimates ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Error ◽  
Navier Stokes Equations ◽  
Element Method

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

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