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Least-squares formulations for Stokes equations with non-standard boundary conditions - A unified approach
  • Subhashree Mohapatra,
  • Naraparaju Kishore Kumar,
  • Shivangi Joshi
Subhashree Mohapatra
Indraprastha Institute of Information Technology Delhi

Corresponding Author:[email protected]

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Naraparaju Kishore Kumar
BITS Pilani - Hyderabad Campus
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Shivangi Joshi
BITS Pilani - Hyderabad Campus
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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.
09 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
10 Sep 2022Submission Checks Completed
10 Sep 2022Assigned to Editor
16 Sep 2022Reviewer(s) Assigned
03 Jan 2023Review(s) Completed, Editorial Evaluation Pending
04 Jan 2023Editorial Decision: Revise Minor
03 Feb 20231st Revision Received
06 Feb 2023Submission Checks Completed
06 Feb 2023Assigned to Editor
06 Feb 2023Review(s) Completed, Editorial Evaluation Pending
06 Feb 2023Reviewer(s) Assigned
16 Mar 2023Editorial Decision: Accept