Stabilized nonconforming finite element methods for data assimilation in incompressible flows

TL;DR

This paper introduces a stabilized nonconforming finite element method with a primal dual structure for data assimilation in incompressible flows governed by Stokes' equations, providing optimal error estimates for ill-posed problems.

Contribution

It develops a novel stabilized nonconforming finite element approach with a primal dual structure for data assimilation in incompressible flows, accommodating nonstandard data.

Findings

Error estimates are optimal relative to the problem's conditional stability.

The method effectively incorporates nonstandard data into the data assimilation process.

The approach enhances stability and accuracy in incompressible flow simulations.

Abstract

We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes' equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data. Error estimates are obtained that are optimal compared to the conditional stability of the ill-posed data assimilation problem.