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Description
| - 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)
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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)
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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)
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skos:notation
| - RIV/67985840:_____/07:00319204!RIV09-AV0-67985840
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA102/05/0629), P(GP201/04/P021), Z(AV0Z10190503), Z(AV0Z20570509)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/67985840:_____/07:00319204
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - discrete maximum principle; hp-FEM; Poisson equation (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - DE - Spolková republika Německo
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Journal of Numerical Mathematics
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Šolín, Pavel
- Vejchodský, Tomáš
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http://linked.open...ain/vavai/riv/wos
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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