Runge-Kutta methods for linear semi-explicit operator differential-algebraic equations

Runge-Kutta methods for linear semi-explicit operator differential-algebraic equations

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 include e.g. the Stokes equations or applications with boundary control. To guarantee u...

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Bibliographic Details
Published in:Mathematics of computation Vol. 87; no. 309; pp. 149 - 174
Main Authors: ALTMANN, R., ZIMMER, C.
Format: Journal Article
Language:English
Published: American Mathematical Society 01-01-2018
Subjects:
Runge-Kutta methods
Operator DAEs
PDAEs
implicit Euler scheme
regularization
Online Access:Get full text
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Summary: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 include 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.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3270