arXiv subjects

Shivangi Joshi

Publications and source records attributed to Shivangi Joshi.

2 recordsLinked to original sources

arXiv2025

Higher-order spectral element method for the stationary Stokes interface problem in two dimensions

This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation. The mesh is aligned with the interface, and the interface is completely resolved using blending element functions. The higher-order spectral element functions are nonconforming, and the same-order approximation is used for both velocity and pressure variables. The interface conditions are added to the minimizing functional in appropriate Sobolev norms. Stability and error estimates are proven. The proposed method is shown to be exponentially accurate in both velocity and pressure variables. The theoretical estimates are validated through various numerical examples.

math.NA↗

arXiv2022

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

In this paper, we propose a unified non-conforming least-squares spectral element approach for solving Stokes equations with various non-standard boundary conditions. Existing least-squares formulations mostly deal with Dirichlet boundary conditions are formulated using ADN theory-based regularity estimates. However, changing boundary conditions lead to a search for parameters satisfying supplementing and complimenting conditions [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.

math.NA↗