EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 58 / No 3 (May-June 2024) ESAIM: M2AN, 58 3 (2024) 1201-1227 References
Open Access
Issue
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
Page(s) 1201 - 1227
DOI https://doi.org/10.1051/m2an/2024026
Published online 27 June 2024
  1. A. Bakhta and V. Ehrlacher, Cross-diffusion systems with non-zero flux and moving boundary conditions. ESAIM Math. Model. Numer. Anal. 52 (2018) 1385–1415. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  2. M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An “empirical interpolation” method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. 339 (2004) 667–672. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.W. Barrett and J.F. Blowey, Finite element approximation of a nonlinear cross-diffusion population model. Numer. Math. 98 (2004) 195–221. [Google Scholar]
  4. T.J. Barth, Numerical methods for gasdynamic systems on unstructured meshes, in An Introduction to Recent Developments in Theory and Numerics for Conservation Laws: Proceedings of the International School on Theory and Numerics for Conservation Laws, Freiburg/Littenweiler, October 20–24, 1997. Springer (1999) 195–285. [Google Scholar]
  5. I. Ben Gharbia, J. Dabaghi, V. Martin and M. Vohralík, A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints. Comput. Geosci. 24 (2020) 1031–1055. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Berkooz, P. Holmes and J.L. Lumley, The proper orthogonal decomposition in the analysis of turbulent flows, in Annual Review of Fluid Mechanics. Vol. 25. Annual Reviews, Palo Alto, CA (1993) 539–575. [Google Scholar]
  7. N. Botta and M. Pandolfi, Upwind formulations for the euler equations in steady supersonic flows. AIAA J. 27 (1989) 293–298. [CrossRef] [Google Scholar]
  8. M. Burger, M. Di Francesco, J.-F. Pietschmann and B. Schlake, Nonlinear cross-diffusion with size exclusion. SIAM J. Math. Anal. 42 (2010) 2842–2871. [CrossRef] [MathSciNet] [Google Scholar]
  9. N. Cagniart, Y. Maday and B. Stamm, Model order reduction for problems with large convection effects, in Contributions to Partial Differential Equations and Applications. Springer (2019) 131–150. [Google Scholar]
  10. C. Cancès and B. Gaudeul, A convergent entropy diminishing finite volume scheme for a cross-diffusion system. SIAM J. Numer. Anal. 58 (2020) 2684–2710. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Cancès, V. Ehrlacher and L. Monasse, Finite volumes for the Stefan–Maxwell cross-diffusion system. IMA J. Numer. Anal. 44 (2024) 1029–1060. [CrossRef] [MathSciNet] [Google Scholar]
  12. S. Chaturantabut, C. Beattie and S. Gugercin, Structure-preserving model reduction for nonlinear port-Hamiltonian systems. SIAM J. Sci. Comput. 38 (2016) B837–B865. [CrossRef] [Google Scholar]
  13. V. Ehrlacher, D. Lombardi, O. Mula and F.-X. Vialard, Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces. ESAIM: Math. Modell. Numer. Anal. 54 (2020) 2159–2197. [CrossRef] [EDP Sciences] [Google Scholar]
  14. S.C. Eisenstat and H.F. Walker, Globally convergent inexact Newton methods. SIAM J. Optim. 4 (1994) 393–422. [CrossRef] [MathSciNet] [Google Scholar]
  15. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in Handbook of Numerical Analysis. Handb. Numer. Anal., VII. Vol. VII. North-Holland, Amsterdam (2000) 713–1020. [CrossRef] [Google Scholar]
  16. L. Fick, Y. Maday, A.T. Patera and T. Taddei, A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection. J. Comput. Phys. 371 (2018) 214–243. [CrossRef] [MathSciNet] [Google Scholar]
  17. R.L. Fox and H. Miura, An approximate analysis technique for design calculations. AIAA J. 9 (1971) 177–179. [CrossRef] [Google Scholar]
  18. Y. Gong, Q. Wang and Z. Wang, Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems. Comput. Methods Appl. Mech. Eng. 315 (2017) 780–798. [CrossRef] [Google Scholar]
  19. M. Gubisch and S. Volkwein, Proper orthogonal decomposition for linear-quadratic optimal control, in Model Reduction and Approximation. Vol. 15 of Comput. Sci. Eng. SIAM, Philadelphia, PA (2017) 3–63. [Google Scholar]
  20. J.S. Hesthaven, C. Pagliantini and N. Ripamonti, Structure-preserving model order reduction of Hamiltonian systems. Preprint arXiv:2109.12367 (2021). [Google Scholar]
  21. J.S. Hesthaven, C. Pagliantini and G. Rozza, Reduced basis methods for time-dependent problems. Acta Numer. 31 (2022) 265–345. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics, Springer, Cham; BCAM Basque Center for Applied Mathematics, Bilbao, BCAM SpringerBriefs (2016). [Google Scholar]
  23. C. Huang, C.R. Wentland, K. Duraisamy and C. Merkle, Model reduction for multi-scale transport problems using model-form preserving least-squares projections with variable transformation. J. Comput. Phys. 448 (2022) 110742. [Google Scholar]
  24. T.L. Jackson and H.M. Byrne, A mechanical model of tumor encapsulation and transcapsular spread. Math. Biosci. 180 (2002) 307–328. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  25. A. Jüngel, The boundedness-by-entropy method for cross-diffusion systems. Nonlinearity 28 (2015) 1963–2001. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Jungel and I.V. Stelzer, Existence analysis of Maxwell–Stefan systems for multicomponent mixtures. SIAM J. Math. Anal. 45 (2013) 2421–2440. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Jüngel and A. Zurek, A finite-volume scheme for a cross-diffusion model arising from interacting many-particle population systems, in International Conference on Finite Volumes for Complex Applications. Springer (2020) 223–231. [Google Scholar]
  28. A. Jüngel and A. Zurek, A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems. IMA J. Numer. Anal. 43 (2023) 560–589. [CrossRef] [MathSciNet] [Google Scholar]
  29. C.T. Kelley, Solving Nonlinear Equations with Newton’S Method. Vol. 1 of Fundamentals of Algorithms. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2003). [Google Scholar]
  30. K. Kergrene, L. Chamoin, M. Laforest and S. Prudhomme, On a goal-oriented version of the proper generalized decomposition method. J. Sci. Comput. 81 (2019) 92–111. [CrossRef] [MathSciNet] [Google Scholar]
  31. K. Kunisch and S. Volkwein, Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition. J. Optim. Theory Appl. 102 (1999) 345–371. [CrossRef] [MathSciNet] [Google Scholar]
  32. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems. Numer. Math. 90 (2001) 117–148. [Google Scholar]
  33. P. Ladevèze and L. Chamoin, On the verification of model reduction methods based on the proper generalized decomposition. Comput. Methods Appl. Mech. Eng. 200 (2011) 2032–2047. [CrossRef] [Google Scholar]
  34. Y. Maday, Reduced basis method for the rapid and reliable solution of partial differential equations, in International Congress of Mathematicians. Vol. III. Eur. Math. Soc., Zürich (2006) 1255–1270. [Google Scholar]
  35. A.K. Noor and J.M. Peters, Reduced basis technique for nonlinear analysis of structures. AIAA J. 18 (1980) 455–462. [CrossRef] [Google Scholar]
  36. A. Nouy, A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Comput. Methods Appl. Mech. Eng. 199 (2010) 1603–1626. [CrossRef] [Google Scholar]
  37. E.J. Parish and F. Rizzi, On the impact of dimensionally-consistent and physics-based inner products for POD-Galerkin and least-squares model reduction of compressible flows. J. Comput. Phys. 491 (2023) 112387. [CrossRef] [Google Scholar]
  38. A. Quarteroni, A. Manzoni and F. Negri, Reduced Basis Methods for Partial Differential Equations: An Introduction. Vol. 92 of Unitext. La Matematica per il 3+2. Springer, Cham (2016). [Google Scholar]
  39. P. Schwerdtner, T. Moser, V. Mehrmann and M. Voigt, Structure-preserving model order reduction for index one port-Hamiltonian descriptor systems. Preprint arXiv:2206.01608 (2022). [Google Scholar]
  40. N. Shigesada, K. Kawasaki and E. Teramoto, Spatial segregation of interacting species. J. Theor. Biol. 79 (1979) 83–99. [CrossRef] [Google Scholar]
  41. G. Welper, Interpolation of functions with parameter dependent jumps by transformed snapshots. SIAM J. Sci. Comput. 39 (2017) A1225–A1250. [Google Scholar]
  42. G. Welper, Transformed snapshot interpolation with high resolution transforms. SIAM J. Sci. Comput. 42 (2020) A2037–A2061. [CrossRef] [Google Scholar]
  43. N. Zamponi and A. Jüngel, Analysis of degenerate cross-diffusion population models with volume filling, in Annales de l’Institut Henri Poincaré C, Analyse non linéaire, Vol. 34. Elsevier (2017) 1–29. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you