Year: 2018
Author: Robert Altmann, Jan Heiland
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 3 : pp. 452–478
Abstract
A general framework for the regularization of constrained PDEs, also called operator differential-algebraic equations (operator DAEs), is presented. The given procedure works for semi-explicit and semi-linear operator DAEs of first order including the Navier-Stokes and other flow equations. The proposed reformulation is consistent, i.e., the solution of the PDE remains untouched. Its main advantage is that it regularizes the operator DAE in the sense that a semi-discretization in space leads to a DAE of lower index. Furthermore, a stability analysis is presented for the linear case, which shows that the regularization provides benefits also for the application of the Rothe method. For this, the influence of perturbations is analyzed for the different formulations. The results are verified by means of a numerical example with an adaptive space discretization.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12525
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 3 : pp. 452–478
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: PDAE operator DAE regularization index reduction Rothe method method of lines perturbation analysis.