Zur Seitenansicht
 

Titelaufnahme

Titel
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions
VerfasserAuzinger, Winfried In der Gemeinsamen Normdatei der DNB nachschlagen ; Koch, Othmar In der Gemeinsamen Normdatei der DNB nachschlagen ; Quell, Michael
Erschienen in
Numerical algorithms, 2016,, S. 1-23
Erschienen2016
Ausgabe
Published version
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Nonlinear evolution equations / Splitting methods / Adaptive time integration / Local error / Convergence
URNurn:nbn:at:at-ubtuw:3-2830 Persistent Identifier (URN)
DOI10.1007/s11075-016-0206-8 
Zugriffsbeschränkung
 Das Werk ist frei verfügbar
Dateien
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions [1.14 mb]
Links
Nachweis
Klassifikation
Zusammenfassung (Englisch)

We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several applications generating intricate patterns and displaying nonsmooth solution dynamics. First, we give a general error analysis for splitting methods for parabolic problems under periodic boundary conditions and derive the necessary smoothness requirements on the exact solution in particular for the GrayScott equation and the Van der Pol equation. Numerical examples demonstrate the convergence of the methods and serve to compare the efficiency of different time-adaptive splitting schemes and of splitting into either two or three operators, based on appropriately constructed a posteriori local error estimators.

Notiz
Lizenz
CC-BY-Lizenz (4.0)Creative Commons Namensnennung 4.0 International Lizenz