Chair for Scientific Computing
RPTU University Kaiserslautern-Landau
Bldg/Geb 34, Paul-Ehrlich-Strasse
67663 Kaiserslautern, Germany
Office: 36-414
Phone: +49 (0)631 205 5643
Fax: +49 (0)631 205 3056
Email: alexander.linke@rptu.de
2026
N. R. Gauger; A. Linke; C. Merdon
Refined stability estimates for mixed problems by exploiting semi norm arguments Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 456, pp. 118928, 2026, ISSN: 0045-7825.
@article{GLMCMAME2026,
title = {Refined stability estimates for mixed problems by exploiting semi norm arguments},
author = {N. R. Gauger and A. Linke and C. Merdon},
url = {https://www.sciencedirect.com/science/article/pii/S004578252600201X},
doi = {doi.org/10.1016/j.cma.2026.118928},
issn = {0045-7825},
year = {2026},
date = {2026-07-01},
urldate = {2026-07-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {456},
pages = {118928},
abstract = {Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible Navier–Stokes equations. In fact, kernels of these semi norms are shown to be connected to physical regimes in applications and are related to some well-known consistency errors in classical discretizations of mixed problems. Consequently, significantly sharper stability estimates for solutions close to these physical regimes are obtained.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible Navier–Stokes equations. In fact, kernels of these semi norms are shown to be connected to physical regimes in applications and are related to some well-known consistency errors in classical discretizations of mixed problems. Consequently, significantly sharper stability estimates for solutions close to these physical regimes are obtained.
V. John; A. Linke; C. Merdon; M. Zainelabdeen
Gradient-robustness for the isentropic compressible Stokes problem Miscellaneous
WIAS Preprint 3286, 2026.
@misc{JLMZWIASPreprint2026,
title = {Gradient-robustness for the isentropic compressible Stokes problem},
author = {V. John and A. Linke and C. Merdon and M. Zainelabdeen},
url = {https://archive.wias-berlin.de/receive/wias_mods_00009826},
doi = {10.20347/WIAS.PREPRINT.3286},
year = {2026},
date = {2026-04-29},
urldate = {2026-04-29},
publisher = {Weierstrass Institute},
abstract = {This paper extends a scheme for the isothermal compressible Stokes problem to the isentropic compressible Stokes problem that has two important ingredients. The first one is a reconstruction operator in the right-hand side that improves the correct balancing of gradient forces in hydrostatic situations. This so-called gradient-robustness makes the scheme asymptotics-preserving (AP) in the zero Mach number limit in the sense that it converges on fixed grids to a pressure-robust scheme for the incompressible Stokes problem. The second ingredient is an AP-compatible stabilization term in the continuity equation that allows a-priori provable strong convergence of the scheme, in particular the satisfaction of the nonlinear barotropic equation of state in the limit. The paper explains the algorithmical details, proves stability and convergence of the scheme as well as meaningful error estimates for the velocity. The results are illustrated by some numerical examples.},
howpublished = {WIAS Preprint 3286},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
This paper extends a scheme for the isothermal compressible Stokes problem to the isentropic compressible Stokes problem that has two important ingredients. The first one is a reconstruction operator in the right-hand side that improves the correct balancing of gradient forces in hydrostatic situations. This so-called gradient-robustness makes the scheme asymptotics-preserving (AP) in the zero Mach number limit in the sense that it converges on fixed grids to a pressure-robust scheme for the incompressible Stokes problem. The second ingredient is an AP-compatible stabilization term in the continuity equation that allows a-priori provable strong convergence of the scheme, in particular the satisfaction of the nonlinear barotropic equation of state in the limit. The paper explains the algorithmical details, proves stability and convergence of the scheme as well as meaningful error estimates for the velocity. The results are illustrated by some numerical examples.
2025
N.R. Gauger, A. Linke, C. Merdon
Refined stability estimates for mixed problems by exploiting semi norm arguments Miscellaneous
arXiv:2506.11566, 2025.
@misc{nokey,
title = {Refined stability estimates for mixed problems by exploiting semi norm arguments},
author = {N.R. Gauger, A. Linke, C. Merdon},
url = {https://arxiv.org/abs/2506.11566},
year = {2025},
date = {2025-06-16},
urldate = {2025-06-16},
abstract = {Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible Navier-Stokes equations. In fact, kernels of these semi norms are shown to be connected to physical regimes in applications and are related to some well-known consistency errors in classical discretizations of mixed problems. Consequently, significantly sharper stability estimates for solutions close to these physical regimes are obtained.},
howpublished = {arXiv:2506.11566},
keywords = {},
pubstate = {published},
tppubtype = {misc}
}
Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible Navier-Stokes equations. In fact, kernels of these semi norms are shown to be connected to physical regimes in applications and are related to some well-known consistency errors in classical discretizations of mixed problems. Consequently, significantly sharper stability estimates for solutions close to these physical regimes are obtained.