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Main Title: Runge-Kutta Methods for Linear Semi-explicit Operator Differential-algebraic Equations
Author(s): Altmann, Robert
Zimmer, Christoph
Type: Research Paper
Abstract: As a first step towards time-stepping schemes for constrained PDE systems, this paper presents convergence results for the temporal discretization of operator DAEs. We consider linear, semi-explicit systems which includes e.g. the Stokes equations or applications with boundary control. To guarantee unique approximations, we restrict the analysis to algebraically stable Runge-Kutta methods for which the stability functions satisfy R(∞)=0. As expected from the theory of DAEs, the convergence properties of the single variables differ and depend strongly on the assumed smoothness of the data.
Subject(s): operator DAEs
Runge-Kutta methods
implicit Euler scheme
Issue Date: 16-Mar-2016
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65J10 Equations with linear operators
65L80 Methods for differential-algebraic equations
65M12 Stability and convergence of numerical methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2016, 10
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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