Recent Publications

• J.-L. Guermond, and B. Popov, Viscous regularization of the Euler equations and entropy principles, SIAM Journal on Applied Mathematics (2014), Vol. 74, No. 2, pp. 284-305.

• 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), pp. 2163–2182.

• B. Popov and V. Tomov, Central schemed for Mean Filed Games, Commun. Math. Sci (2015), Vol. 13, No.8, pp. 2177-2194.

• J.-L. Guermond and B. Popov, Error estimates of a first-order Lagrange finite element technique for nonlinear scalar conservation equations, SIAM J. Numer. Anal. 54 (2016), pp. 57–85.

• J.-L. Guermond, B. Popov and V. Tomov, Entropy Viscosity Method for the Single Material Euler Equations in Lagrangian Frame, Computer Methods in Applied Mechanics and Engineering  (2016), Vol. 300, No.1, pp. 402-426.

• J.-L. Guermond, and B. Popov, Invariant domains and first-order continuous finite element approximation for hyperbolic systems,  SIAM J. Numer. Anal. 54 (2016), pp. 2466 - 2489.
  

• J.-L. Guermond, and B. Popov, Fast estimation of the maximum wave speed in the Riemann problem for the Euler equations,  J. Comput. Phys. 321 (2016), pp  908 - 926.
  

• J.-L. Guermond, B. Popov, L. Saavedra, and Y. Yang, Invariant domains preserving ALE approximation of hyperbolic systems with continuous finite elements, SIAM J. Sci. Comput. 39 (2017), no.2, A385 - A414.
  

• J.-L. Guermond, B. Popov, and Y. Yang, The effect of the consistent mass matrix on the maximum principle for scalar conservation equations, J. Sci. Comput. 70 (2017), pp. 1358 - 1366.
  

• P. Azerad, J.-L. Guermond, B. Popov, Well-balanced second-order approximation  of the shallow water equation with continuous finite elements, SIAM J. Numer. Anal. 55:6 (2017)  3203--3224.
• J.-L. Guermond  and  B. Popov, Invariant domains and second-order continuous finite element approximation for scalar conservation equations,  SIAM J. Numer. Anal. 55:6 (2017) 3120--3146.
• J.-L.GUERMOND, M. NAZAROV, B. POPOV, I. Tomas, Second-order invariant domain preserving approximation of the Euler equations using convex limiting, (supplementary), SIAM J. Sci. Comput., 40  5 (2018) A3211--A3239.
  
• J.-L.GUERMOND, B. POPOV, LAURA SAAVEDRA, YONG YANG, Arbitrary Lagrangian-Eulerian Finite Element Method Preserving Convex Invariants of Hyperbolic Systems, in Contributions to Partial Differential Equations and Applications, Chetverushkin, B. N., Fitzgibbon, W., Kuznetsov, Y.A., Neittaanmaki, P., Periaux, J., Pironneau, O., Eds., Springer International Publishing, (2019) 251--272.
• J.-L. Guermond, B. Popov, I. Tomas, Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems, Computer Methods in Applied Mechanics and Engineering  (2019), Vol. 347, No.15, 143-175.  
• J.-L. Guermond, C. Klingenberg, B. Popov, I. Tomas, The Suliciu approximate Riemann solver is not invariant domain preserving, J. Hyperbolic  Differ. Equ., 16 (2019), no. 1, 59-72.
• Guermond, Jean-Luc; Popov, Bojan; Saavedra, Laura; Second-order invariant domain preserving ALE approximation of hyperbolic systems. J. Comput. Phys. 401 (2020).
• Guermond, Jean-Luc; Popov, Bojan; Tovar, Eric; Kees, Chris; Robust explicit relaxation technique for solving the Green-Naghdi equations. J. Comput. Phys. 399 (2019).
• J.-L. Guermond, B. Popov, J. Ragusa; Positive asymptotic preserving approximation of the radiation transport equation, SIAM J. Numer. Anal. (2019).