Bänsch E, Morin P, Nochetto R (2002)
Publication Type: Journal article
Publication year: 2002
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 40
Pages Range: 1207-1229
Journal Issue: 4
DOI: 10.1137/S0036142901392134
We introduce and study an adaptive finite element method (FEM) for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity, whereas for pressure the elements can be either discontinuous of degree k - 1 or continuous of degree k -1 and k. The popular Taylor-Hood family is the sole example of stable elements included in the theory, which in turn relies on the stability of the continuous problem and thus makes no use of the discrete inf-sup condition. We discuss the realization and complexity of the elliptic adaptive inner solver and provide consistent computational evidence that the resulting meshes are quasi-optimal.
APA:
Bänsch, E., Morin, P., & Nochetto, R. (2002). An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition. SIAM Journal on Numerical Analysis, 40(4), 1207-1229. https://doi.org/10.1137/S0036142901392134
MLA:
Bänsch, Eberhard, Pedro Morin, and Ricardo Nochetto. "An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition." SIAM Journal on Numerical Analysis 40.4 (2002): 1207-1229.
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