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\begin{document}

\title{Least-squares formulations for Stokes equations with non-standard
boundary conditions - A unified approach}



\author[1]{Subhashree Mohapatra}%
\author[2]{Naraparaju Kishore Kumar}%
\author[2]{Shivangi Joshi}%
\affil[1]{Indraprastha Institute of Information Technology Delhi}%
\affil[2]{BITS Pilani - Hyderabad Campus}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
In this paper, we propose a unified non-conforming least-squares
spectral element ap- proach for solving Stokes equations with various
non-standard boundary conditions. Ex- isting least-squares formulations
mostly deal with Dirichlet boundary conditions and are formulated using
ADN theory based regularity estimates. However, changing boundary
conditions lead to a search for parameters satisfying supplementing and
complimenting con- ditions {[}4{]} which is not easy always. Here we
have avoided ADN theory based regularity estimates and proposed a
unified approach for dealing with various boundary conditions. Stability
estimates and error estimates have been discussed. Numerical results
displaying exponential accuracy have been presented for both two and
three dimensional cases with various boundary conditions.%
\end{abstract}%



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