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Preprint 10-2016

Runge-Kutta Methods for Linear Semi-explicit Operator Differential-algebraic Equations

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Author(s) : Robert Altmann , Christoph Zimmer

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2016

MSC 2000

65J10 Equations with linear operators
65L80 Methods for differential-algebraic equations
65M12 Stability and convergence of numerical methods

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(\infty)=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.

Keywords : operator DAEs, PDAEs, Runge-Kutta methods, implicit Euler scheme, regularization

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