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