Free Access
Issue
ESAIM: M2AN
Volume 53, Number 5, September-October 2019
Page(s) 1629 - 1644
DOI https://doi.org/10.1051/m2an/2018046
Published online 12 August 2019
  1. W. Bangerth, R. Hartmann and G. Kanschat, deal.II – a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33 (2007) 24/1–24/27. [CrossRef] [Google Scholar]
  2. C. Bardos, A.Y. Leroux and J.C. Nedelec, First order quasilinear equations with boundary conditions. Commun. Part. Diff. Eq. 4 (Jan 1979) 1017–1034. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Bates, J. Hauenstein, A. Sommese and C. Wampler, Numerically Solving Polynomial Systems with Bertini (Software, Environments and Tools). SIAM, Philadelphia, Pennsylvania (2013). [Google Scholar]
  4. A. Ern and J.L. Guermond, Theory and Practice of Finite Elements. Applied Mathematical Sciences. Springer, New York (2004). [CrossRef] [Google Scholar]
  5. L.C. Evans, Partial Differential Equations, in Vol. 19 of Graduate Studies in Mathematics. Providence, Rhode Island (1998). [Google Scholar]
  6. J.-L. Guermond and M. Nazarov, A maximum-principle preserving # finite element method for scalar conservation equations. Comput. Methods Appl. Mech. Engrg. 272 (2014) 198–213. [CrossRef] [Google Scholar]
  7. J.-L. Guermond and B. Popov, Invariant domains and first-order continuous finite element approximation for hyperbolic systems. SIAM J. Numer. Anal. 54 (2016) 2466–2489. [CrossRef] [Google Scholar]
  8. J.-L. Guermond, R. Pasquetti and B. Popov, Entropy viscosity method for nonlinear conservation laws. J. Comput. Phys. 230 (2011) 4248–4267. [CrossRef] [Google Scholar]
  9. J.-L. Guermond, M. Nazarov, B. Popov and Y. Yang, A second-order maximum principle preserving Lagrange finite element technique for nonlinear scalar conservation equations. SIAM J. Numer. Anal. 52 (2014) 2163–2182. [CrossRef] [Google Scholar]
  10. W. Hao, J. Hauenstein, B. Hu, Y. Liu, A. Sommese and Y.-T. Zhang, Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. Nonlinear Anal. Real World App. 13 (2012) 694–709. [CrossRef] [Google Scholar]
  11. W. Hao, J. Hauenstein, B. Hu, T. McCoy and A. Sommese, Computing steady-state solutions for a free boundary problem modeling tumor growth by stokes equation. J. Comput. Appl. Math. 237 (2013) 326–334. [CrossRef] [Google Scholar]
  12. W. Hao, J. Hauenstein, C.-W. Shu, A. Sommese, Z. Xu and Y.-T. Zhang, A homotopy method based on weno schemes for solving steady state problems of hyperbolic conservation laws. J. Comput. Phys. 250 (2013) 332–346. [Google Scholar]
  13. W. Hao, R. Nepomechie and A. Sommese, Completeness of solutions of bethe’s equations. Phys. Rev. E 88 (2013) 052113. [Google Scholar]
  14. W. Hao, B. Hu and A. Sommese, Numerical algebraic geometry and differential equations. In: Future Vision and Trends on Shapes, Geometry and Algebra. Springer, London (2014) 39–53. [Google Scholar]
  15. J. Hicken and D. Zingg, Globalization strategies for inexact-newton solvers. In: 19th AIAA Computational Fluid Dynamics (2009) 4139. [Google Scholar]
  16. J. Hicken, H. Buckley, M. Osusky and D. Zingg, Dissipation-based continuation: a globalization for inexact-newton solvers. In: 20th AIAA Computational Fluid Dynamics Conference (2011) 3237. [Google Scholar]
  17. E. Hopf, The partial differential equation #. Commun. Pure App. Math. 3 (1950) 201–230. [CrossRef] [MathSciNet] [Google Scholar]
  18. A.F. Izmailov and M.V. Solodov, Newton-Type Methods for Optimization and Variational Problems. Springer Series in Operations Research and Financial Engineering. Springer International Publishing, New York (2014). [CrossRef] [Google Scholar]
  19. G. Kreiss and H.-O. Kreiss, Convergence to steady state of solutions of Burgers’ equation. Appl. Numer. Math. 2 (1986) 161–179. [CrossRef] [Google Scholar]
  20. P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954) 159–193. [CrossRef] [MathSciNet] [Google Scholar]
  21. V.B. Leer, Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme. J. Comput. Phys. 14 (1974) 361–370. [NASA ADS] [CrossRef] [Google Scholar]
  22. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. (1990) 408–463. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  23. M.D. Salas, S. Abarbanel and D. Gottlieb, Multiple steady states for characteristic initial value problems. Appl. Numer. Math. 2 (1986) 193–210. [CrossRef] [Google Scholar]
  24. A. Sommese and C. Wampler, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. In Vol. 99. World Scientific, Singapore. (2005). [Google Scholar]
  25. I.S. Strub and A.M. Bayen, Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling. Int. J. Robust Nonlin. Control 16 (2006) 733–748. [CrossRef] [Google Scholar]

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