Lu Zhang

Mean-Field Games:

  1. Q. Wang, Y. Xiong and L. Zhang. Well-posedness, convergence and stability of finite difference methods for mean-field games, preprint

Data-Driven Computations:

  1. K. Ren and L. Zhang. Data-driven joint inversions for PDE models, link
  2. W. Ding, K. Ren and L. Zhang. Coupling deep learning with full waveform inversion, link
  3. Q. Wang, L. Zhang and Q. Zhang. GARCH-PDE models for option pricing under stochastic volatility and their finite difference solvers, preprint

High-order Numerical Methods:

  1. Q. Wang, L. Zhang. An energy-based discontinuous Galerkin method for stochastic wave equations, preprint
  2. L. Zhang. A fully discrete energy-based discontinuous Galerkin method for variable-order time fractional wave equations, preprint
  3. Q. Du, H. Li, M. Weinstein, L. Zhang. Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array, link, J. Sci. Comput. 101(3), 1-34 (2024)
  4. K. Ren, L. Zhang, Y. Zhou. An energy-based discontinuous Galerkin method for the nonlinear Schrodinger equation with wave operator, link, SIAM J. Numer. Anal. (62)6, 2459-2483 (2024)
  5. Q. Wang, L. Zhang. An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations, link, ESAIM: M2AN, 58, 1725–1754 (2024)
  6. L. Zhang. A local energy-based discontinuous Galerkin method for fourth order semilinear wave equations, link, IMA J. Numeri. Anal. 44(5), 2793-2820 (2024)
  7. D. Appelo, L. Zhang, T. Hagstrom and F. Li. An energy-based discontinuous Galerkin method with Tame CFL numbers for the wave equation, BIT Numer. Math., 63(1), 5, (2023), link
  8. L. Zhang and S. Wang. A high order finite difference method for the elastic wave equation in bounded anisotropic and discontinuous media, SIAM J. Numer. Anal., 60(3), 1516-1547 (2022), link
  9. L. Zhang, D. Appelo and T. Hagstrom. Energy-based discontinuous Galerkin difference methods for second-order wave equations, Comm. Appl. Math. Comput. (2022), link
  10. T. Hagstrom, D. Appelo, and L. Zhang. Discontinuous Galerkin methods for electromagnetic waves in dispersive media, 2021 International Applied Computational Electromagnetics Society Symposium (ACES), pp.1-4(2021), link
  11. L. Zhang, S. Wang and N.A. Petersson. Elastic wave propagation in curvilinear coordinates with mesh refinement interfaces by a fourth order finite difference method, SIAM J. Sci. Comput., 43(2), A1472-A1496 (2021), link
  12. D. Appelo, T. Hagstrom, Q. Wang and L. Zhang. An energy-based discontinuous Galerkin method for semilinear wave equations, J. Comput. Phys., 418(2020), link
  13. L. Zhang, T. Hagstrom and D. Appelo. An energy-based discontinuous Galerkin method for the wave equation with advection, SIAM J. Numer. Anal., 57(5), 2469-2492(2019), link
  14. Y. Du, L. Zhang and Z. Zhang. Convergence analysis of a discontinuous Galerkin method for wave equations in second-order form, SIAM J. Numer. Anal., 57(1), 238-265(2019), link

Applied PDEs:

  1. N. Rodriguez, Q. Wang, and L. Zhang. Understanding the effects of on- and off-hotspot policing: Evidence of hotspot, oscillating and chaotic activities, SIAM J. Appl. Dyn. Syst.,20(4), 1882-1916 (2021), link
  2. J. A. Carrillo, X. Chen, Q. Wang, Z. Wang and L. Zhang. Phase transitions and bump solutions of the Keller-Segel model with volume exclusion, SIAM J. Appl. Math., 80(1), 232-261(2020), link
  3. Q. Wang, J. Yang, and L. Zhang. Time–periodic and stable patterns of two–competing Keller–Segel chemotaxis model: Effect of cellular growth, Discrete Contin. Dyn. Syst. Ser. B, 22(9), 3547-3574(2017), link
  4. Q. Wang, and L. Zhang. On the multi–dimensional advective Lotka–Volterra competition systems, Nonlinear Anal. Real World Appl., 37, 329-349(2017), link
  5. Q. Wang, L. Zhang, J. Yang and J. Hu. Global existence and steady states of a two competing species Keller–Segel chemotaxis model, Kinet. Relat. Models, 8(4), 777-807(2015), link