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In this paper, we propose a unified non-conforming least-squares spectralelement approach for solving Stokes equations with various non-standardboundary conditions. Existing least-squares formulations mostly deal withDirichlet boundary conditions are formulated using ADN theory-based regularityestimates. However, changing boundary conditions lead to a search forparameters satisfying supplementing and complimenting conditions [4] which isnot easy always. Here we have avoided ADN theory-based regularity estimates andproposed a unified approach for dealing with various boundary conditions.Stability estimates and error estimates have been discussed. Numerical resultsdisplaying exponential accuracy have been presented for both two andthree-dimensional cases with various boundary conditions.

Least-squares formulations for Stokes equations with non-standard boundary conditions -- A unified approach