Volume 15, Issue 3
Regularization and Rothe Discretization of Semi-Explicit Operator DAEs

Robert Altmann & Jan Heiland

Int. J. Numer. Anal. Mod., 15 (2018), pp. 452-478.

Published online: 2018-03

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  • 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.

  • Keywords

PDAE, operator DAE, regularization, index reduction, Rothe method, method of lines, perturbation analysis.

  • AMS Subject Headings

65J08, 65M12, 65L80.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

robert.altmann@math.uni-augsburg.de (Robert Altmann)

heiland@mpi-magdeburg.mpg.de (Jan Heiland)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-452, author = {Altmann , Robert and Heiland , Jan}, title = {Regularization and Rothe Discretization of Semi-Explicit Operator DAEs}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12525.html} }
TY - JOUR T1 - Regularization and Rothe Discretization of Semi-Explicit Operator DAEs AU - Altmann , Robert AU - Heiland , Jan JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 452 EP - 478 PY - 2018 DA - 2018/03 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12525.html KW - PDAE, operator DAE, regularization, index reduction, Rothe method, method of lines, perturbation analysis. AB -

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.

Robert Altmann & Jan Heiland. (2019). Regularization and Rothe Discretization of Semi-Explicit Operator DAEs. International Journal of Numerical Analysis and Modeling. 15 (3). 452-478. doi:
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