On the time growth of the error of the DG method for advective problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10406741" target="_blank" >RIV/00216208:11320/19:10406741 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6gb7KqfH88" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6gb7KqfH88</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imanum/dry013" target="_blank" >10.1093/imanum/dry013</a>

Result language
angličtina
Original language name
On the time growth of the error of the DG method for advective problems
Original language description
In this paper we derive a priori L-infinity(L-2) and L-2(L-2) error estimates for a linear advection-reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall's inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some (T) over cap, we derive O(h(p+1/2)) error estimates where the constant factor depends only on (T) over cap, but not on the final time T. This can be interpreted as applying Gronwall's inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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