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  • V tomto članku dokazujeme novy diskrétní princip maxima (DMP) pro jednorozměrnou Poissonovu rovnici diskretizovanou pomoci hp-FEM. Zatímco DMP pro po částech lineární prvky je klasicky výsledek ze sedmdesátých let, rozšířit tento výsledek na hp-FEM se dosud nikomu nepodařilo. Na základě negativniho vysledku prezentovaného v roce 1981 Hoehnem a Mittelmannem se všeobecně předpokládalo, že takove rozšířeni není možné. V tomto članku vysvětlujeme, proč není možné přímé zobecnění klasického DMP a navrhujeme silnější předpoklady na pravou stranu, za nichž je zobecněni proveditelne. (cs)
  • In this paper we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM have been available to the present day. Due to a negative result by Hoehn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible.
  • In this paper we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM have been available to the present day. Due to a negative result by Hoehn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible. (en)
Title
  • On a Weak Discrete Maximum Principle for hp-FEM
  • On a Weak Discrete Maximum Principle for hp-FEM (en)
  • Slabý diskrétní princip maxima pro hp-FEM (cs)
skos:prefLabel
  • On a Weak Discrete Maximum Principle for hp-FEM
  • On a Weak Discrete Maximum Principle for hp-FEM (en)
  • Slabý diskrétní princip maxima pro hp-FEM (cs)
skos:notation
  • RIV/67985840:_____/07:00044977!RIV08-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 54;65
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA102/05/0629), Z(AV0Z10190503), Z(AV0Z20570509)
http://linked.open...iv/cisloPeriodika
  • 209
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 439177
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/07:00044977
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • discrete maximum principle; hp-FEM (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [C2DFD69BBE16]
http://linked.open...i/riv/nazevZdroje
  • Journal of Computational and Applied Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • -
http://linked.open...iv/tvurceVysledku
  • Šolín, Pavel
  • Vejchodský, Tomáš
http://linked.open...n/vavai/riv/zamer
issn
  • 0377-0427
number of pages
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