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Date
2000-06Type
- Report
ETH Bibliography
yes
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Abstract
We consider the hp-version of the discontinuous Galerkin finite element method for second-order partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic equations, first-order hyperbolic equations, as well as problems of mixed hyperbolic-elliptic-parabolic type. Our main concern is the error analysis of the method in the absence of streamline-diffusion stabilization. In the hyperbolic case, an hp-optimal error bound is derived. In the self-adjoint elliptic case, an error bound that is h-optimal and p-suboptimal by 1/2 a power of p is obtained. These estimates are then combined to deduce an error bound in the general case. For element-wise analytic solutions the method exhibits exponential rates of convergence under p-refinement. The theoretical results are illustrated by numerical experiments. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004288574Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
hp-finite element methods; discontinuous Galerkin methods; PDEs with nonnegative characteristic formOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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ETH Bibliography
yes
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