In this talk, we consider *p* and *h-p* least-squares spectral element methods for elliptic boundary layer problems in one dimension. We derive stability
estimates and design a numerical scheme based on minimizing the residuals in the sense of least-squares in appropriate Sobolev norms. We prove parameter
robust uniform error estimates i.e. error in the approximation is independent of the boundary layer parameter for the *p* and *hp*-version. Numerical results
are presented for a number of model elliptic boundary layer problems confirming the theoretical estimates and uniform convergence results.

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Last updated: 08 Oct 2024