An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms

Barrios, Tomás P.; Behrens, Edwin M.; Bustinza, Rommel

doi:10.1007/s10444-021-09906-2

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…Several approaches have been considered to design error estimators based on the residual equations (see [1,40] and the references therein). In particular, for the load problem associated to the Stokes equations, we can mention as recent developments [7,30,37], whereas for the Stokes spectral problems we refer to [5,23,29,39], and the references therein. Now, following with our research program related to mixed formulations and their discretizations for eigenvalue problems, the present work introduces a formulation that is inspired in [18] for the load problem, where an augmented method is introduced in order to approximate the velocity, pressure and stress.…”

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confidence: 99%

Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem

Lepe¹,

Rivera²,

Vellojin³

2022

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The aim of this paper is to analyze a mixed formulation for the two dimensional Stokes eigenvalue problem where the unknowns are the stress and the velocity, whereas the pressure can be recovered with a simple postprocess of the stress. The stress tensor is written in terms of the vorticity of the fluid, leading to an alternative mixed formulation that incorporates this physical feature. We propose a mixed numerical method where the stress is approximated with suitable Nédelec finite elements, whereas the velocity is approximated with piecewise polynomials of degree k ≥ 0. With the aid of the compact operators theory we derive convergence of the method and spectral correctness. Moreover, we propose a reliable and efficient a posteriori error estimator for our spectral problem. We report numerical tests in different domains, computing the spectrum and convergence orders, together with a computational analysis for the proposed estimator. In addition, we use the corresponding error estimator to drive an adaptive scheme, and we report the results of a numerical test, that allow us to assess the performance of this approach.

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