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  • In this paper we prove the discrete maximum principle for a one-dimensional equation of the form - (au´)´= f with piecewise-constant coefficient a(x), discretized by the hp-FEM. The discrete problem is transformed in such a way that the discontinuity of the coefficient a (x) disappears. Existing results are then applied to obtain a condition on the mesh which guarantees the satisfaction of the discrete maximum principle. Both Dirichlet and mixed Dirichlet-Neumann boundary conditions are discussed.
  • In this paper we prove the discrete maximum principle for a one-dimensional equation of the form - (au´)´= f with piecewise-constant coefficient a(x), discretized by the hp-FEM. The discrete problem is transformed in such a way that the discontinuity of the coefficient a (x) disappears. Existing results are then applied to obtain a condition on the mesh which guarantees the satisfaction of the discrete maximum principle. Both Dirichlet and mixed Dirichlet-Neumann boundary conditions are discussed. (en)
  • V tomto článku dokazujeme diskrétní princip maxima pro jednorozměrnou rovnici ve tvaru -(au´)´= f s po částech konstantním koeficientem a(x) diskretizovaným hp-verzí metody konečných prvků. Diskrétní úloha se transformuje takovým způsobem, že nespojitost koeficientu a(x) zmizí. Potom se aplikuje známý výsledek pro Poissonovu rovnici a obdrží se podmínky, které zaručují splnění diskrétního principu maxima. Oboje Dirichletovy i Neumannovy okrajové podmínky jsou studovány. (cs)
Title
  • Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM
  • Diskrétní princip maxima, pro 1D úlohu s po částech konstantními koeficienty řešenou hp-verzí metody konečných prvků (cs)
  • Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM (en)
skos:prefLabel
  • Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM
  • Diskrétní princip maxima, pro 1D úlohu s po částech konstantními koeficienty řešenou hp-verzí metody konečných prvků (cs)
  • Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM (en)
skos:notation
  • RIV/67985840:_____/07:00319204!RIV09-AV0-67985840
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA102/05/0629), P(GP201/04/P021), Z(AV0Z10190503), Z(AV0Z20570509)
http://linked.open...iv/cisloPeriodika
  • 3
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
  • 417493
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/07:00319204
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • discrete maximum principle; hp-FEM; Poisson equation (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [20804C1DDE1C]
http://linked.open...i/riv/nazevZdroje
  • Journal of Numerical 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
  • 15
http://linked.open...iv/tvurceVysledku
  • Šolín, Pavel
  • Vejchodský, Tomáš
http://linked.open...ain/vavai/riv/wos
  • 000258956700004
http://linked.open...n/vavai/riv/zamer
issn
  • 1570-2820
number of pages
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