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Date
1997-02Type
- Report
ETH Bibliography
yes
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Abstract
We analyze an hp FEM for convection-diffusion problems. Stability is achieved by suitably upwinded test functions, generalizing the classical $\alpha$-quadratically upwinded and the Hemker test-functions for piecewise linear trial spaces (see, e.g., [12] and the references there). The method is proved to be stable independently of the viscosity. Further, the stability is shown to depend only weakly on the spectral order. We show how sufficiently accurate, approximate upwinded test functions can be computed on each element by a local least squares FEM. Under the assumption of analyticity of the input data, we prove robust exponential convergence of the method. Numerical experiments confirm our convergence estimates and show robust exponential convergence of the hp-FEM even for viscosities of the order of machine precision, i.e., for the limiting transport problem. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004284603Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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ETH Bibliography
yes
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