Open access
Date
2011-02Type
- Report
ETH Bibliography
yes
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Abstract
We propose a general framework for well posed variational formulations of linear unsymmetric operators, taking first order transport \cs{and evolution} equations in bounded domains as primary orientation. We outline a general variational framework for stable discretizations of boundary value problems for these operators. To adaptively resolve anisotropic solution features such as propagating singularities the variational formulations should allow one, in particular, to employ as trial spaces directional representation systems. Since such systems are known to be stable in $L_2$ special emphasis is placed on $L_2$-stable formulations. The proposed stability concept is based on perturbations of certain "ideal" test spaces in Petrov-Galerkin formulations. We develop a general strategy for realizing corresponding schemes without actually computing excessively expensive test basis functions. Moreover, we develop adaptive solution concepts with provable error reduction. The results are illustrated by first numerical experiments. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010401913Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Linear transport problems; L2-stable Petrov-Galerkin formulations; Trace theorems; δ-proximality; Adaptive refinement schemes; Rresidual approximation; Error reductionOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Related publications and datasets
Is original form of: http://hdl.handle.net/20.500.11850/57678
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ETH Bibliography
yes
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