Local discontinuous Galerkin methods for the Stokes system
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Date
2000-11
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Report
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Abstract
In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For arbitrary meshes with hanging nodes and elements of various shapes we derive a priori estimates for the L^2-norm of the errors in the velocities and the pressure. We show that optimal order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k-1 for the pressure, for any k \ge 1 . We also consider the case in which all the unknowns are approximated with polynomials of degree k and show that, although the orders of convergence remain the same, the method is more efficient. Numerical experiments verifying these facts are displayed.
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published
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Volume
2000-14
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Finite elements; discontinuous Galerkin methods; Stokes system
Organisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
03435 - Schwab, Christoph / Schwab, Christoph