Rosenbrock-Type Methods for Semilinear Parabolic Equations

In this work we examine the viability of Rosenbrock-type time-stepping methods - specifically Rosenbrock-Wanner (ROW) methods and W-methods - for the temporal discretization of certain parabolic partial differential equations (PDEs) that have a dominating linear term (usually the Laplacian) and lower order nonlinearities, such as convective or reactive terms.

In dieser Arbeit untersuchen wir die Eignung von Rosenbrock-Typ-Methoden (RTM) - speziell von Rosenbrock-Wanner- (ROW) und W-Methoden - für die zeitliche Diskretisierung von bestimmten parabolischen partiellen Differentialgleichungen (PDG), die einen dominierenden linearen Term haben (z. B. den Laplace-Operator) und Nichtlinearitäten niedrigerer Ordnung, wie z. B. konvektive oder reaktive Terme.

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Translated title:
Rosenbrock-Typ-Methoden für semilineare parabolische Gleichungen (German)
Thesis advisor:
Prof. Dr. Braack, Malte
Reviewer:
Prof. Dr. Lang, Jens
Date of oral exam:
04.11.2019
Date Issued:
2019
URN:
urn:nbn:de:gbv:8-diss-263145
Language:
English
Type of Resource:
Text
Keywords:
Numerical analysis; Nonlinear parabolic problems; Rosenbrock-type methods; Computational fluid dynamics; Incompressible Navier-Stokes equations; Numerische Analysis; Nichtlineare parabolische Probleme; Rosenbrock-Typ-Methoden; Numerische Strömungsmechanik; Inkompressible Navier-Stokes-Gleichungen
DDC subject of DNB:
510 Mathematics
Hosting institution:
Faculties, Faculty of Mathematics and Natural Sciences

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