About: Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We present a new class of adaptivity algorithms for time-dependent partial differential equations (PDE) that combine adaptive higher-order finite elements (hp-FEM) in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time. Weak formulation is only created for the stationary residual, and the Runge-Kutta methods are specified via their Butcher's tables. Around 30 Butcher's tables for various Runge-Kutta methods with numerically verified orders of local and global truncation errors are provided. A time-dependent benchmark problem with known exact solution that contains a sharp moving front is introduced, and it is used to compare the quality of seven embedded implicit higher-order Runge-Kutta methods. Numerical experiments also include a comparison of adaptive low-order FEM and hp-FEM with dynamically changing meshes. All numerical results presented in this paper were obtained using the open source library Hermes (http://www.hpfem.org/hermes) and they are reproducible in the Networked Computing Laboratory (NCLab) at http://www.nclab.com. (C) 2011 Elsevier Inc. All rights reserved. We present a new class of adaptivity algorithms for time-dependent partial differential equations (PDE) that combine adaptive higher-order finite elements (hp-FEM) in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time. Weak formulation is only created for the stationary residual, and the Runge-Kutta methods are specified via their Butcher's tables. Around 30 Butcher's tables for various Runge-Kutta methods with numerically verified orders of local and global truncation errors are provided. A time-dependent benchmark problem with known exact solution that contains a sharp moving front is introduced, and it is used to compare the quality of seven embedded implicit higher-order Runge-Kutta methods. Numerical experiments also include a comparison of adaptive low-order FEM and hp-FEM with dynamically changing meshes. All numerical results presented in this paper were obtained using the open source library Hermes (http://www.hpfem.org/hermes) and they are reproducible in the Networked Computing Laboratory (NCLab) at http://www.nclab.com. (C) 2011 Elsevier Inc. All rights reserved. (en)
Title	Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods (en)
skos:prefLabel	Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods (en)
skos:notation	RIV/61388998:_____/12:00438628!RIV15-AV0-61388998
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100760702), Z(AV0Z20760514)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Šolín, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav termomechaniky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	121048
http://linked.open...ai/riv/idVysledku	RIV/61388998:_____/12:00438628
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Runge-Kutta method; Butcher's table; finite element method (en)
http://linked.open.../riv/klicoveSlovo	Runge-Kutta method finite element method Butcher's table
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[F4E579E9F9BA]
http://linked.open...i/riv/nazevZdroje	Journal of Computational Physics
http://linked.open...in/vavai/riv/obor	JA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Methods of higher order of accuracy for solution of multi-physics coupled problems
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	231
http://linked.open...iv/tvurceVysledku	Šolín, Pavel Korous, L.
http://linked.open...ain/vavai/riv/wos	000300462100028
http://linked.open...n/vavai/riv/zamer	Complex dynamical systems in thermodynamics, fluid and solid mechanics
issn	0021-9991
number of pages	15 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jcp.2011.10.023

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