Geodesic
On polynomial robustness of flux reconstructions
Applications of Mathematics, Tome 65 (2020) no. 2, pp. 153-172 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on $p^{1/2}$ only, where $p$ is the discretization polynomial degree. The theoretical results are verified by numerical experiments.
We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on $p^{1/2}$ only, where $p$ is the discretization polynomial degree. The theoretical results are verified by numerical experiments.
DOI : 10.21136/AM.2020.0152-19
Classification : 65N15, 65N30
Keywords: a posteriori error estimate; $p$-robustness; elliptic problem 
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     author = {Vlas\'ak, Miloslav},
     title = {On polynomial robustness of flux reconstructions},
     journal = {Applications of Mathematics},
     pages = {153--172},
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     number = {2},
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     mrnumber = {4083462},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0152-19/}
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Vlasák, Miloslav. On polynomial robustness of flux reconstructions. Applications of Mathematics, Tome 65 (2020) no. 2, pp. 153-172. doi: 10.21136/AM.2020.0152-19

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