Error analysis of a DG method employing ideal elements applied to a nonlinear convection-diffusion problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00182386" target="_blank" >RIV/68407700:21230/11:00182386 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/JNUM.2011.007" target="_blank" >http://dx.doi.org/10.1515/JNUM.2011.007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/JNUM.2011.007" target="_blank" >10.1515/JNUM.2011.007</a>

Result language
angličtina
Original language name
Error analysis of a DG method employing ideal elements applied to a nonlinear convection-diffusion problem
Original language description
In this paper we use the discontinuous Galerkin finite element method for the space-semidiscretization of a nonlinear nonstationary convection-diffusion problem defined on a nonpolygonal two-dimensional domain. Using Zlámal's concept of the ideal curvedelements, we define a finite element space . We prove the 'ideal' versions of the inverse and the multiplicative trace inequalities known for standard straight triangulations. Further, we define a projection on the finite element space and study its approximation properties. The obtained results allow us to derive an H1-optimal error estimate for the discontinuous Galerkin method employing the ideal curved elements.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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