Under Review: L. Liu, L. Zhang and A. Gelb. Parametric hyperbolic conservation laws: A unified framework for conservation, entropy stability, and hyperbolicity Q. Du, K. Ren, L. Zhang and Y. Zhou. A discontinuous Galerkin method for one-dimensional nonlocal wave problems L. Zhang. A fully discrete energy-based discontinuous Galerkin method for variable-order time fractional wave equations Q. Wang, Y. Xiong and L. Zhang. Well-posedness, convergence and stability of finite difference methods for mean-field games Published: L. Liu, L. Zhang and A. Gelb. Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws, accepted by J. Comput. Phys. Q. Wang, L. Zhang and Q. Zhang. GARCH-PDE models for option pricing under stochastic volatility and their finite difference solvers, accepted by J. Finance and Data Sci. W. Ding, K. Ren and L. Zhang. Coupling deep learning with full waveform inversion, link, accepted by Handb. Numer. Anal. Y. Pan, Q. Wang and L. Zhang. Identification of nonconcave aggregate production functions in spatial Solow models with technology diffusion, link, SIAM J. Appl. Math., 2026 K. Ren and L. Zhang. A model-consistent data-driven computational strategy for PDE joint inversion problems, link, J. Comput. Phys., 2025 Q. Wang, L. Zhang. An ultraweak-local discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations, link, ESAIM: M2AN, 58, 1725–1754, 2024 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 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 L. Zhang. A local energy-based discontinuous Galerkin method for fourth order semilinear wave equations, link, IMA J. Numeri. Anal. 44(5), 2793-2820, 2023 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 L. Zhang, D. Appelo and T. Hagstrom. Energy-based discontinuous Galerkin difference methods for second-order wave equations, Comm. Appl. Math. Comput., 2022 link 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 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 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 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, link 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 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 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 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 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 Q. Wang, and L. Zhang. On the multi–dimensional advective Lotka–Volterra competition systems, Nonlinear Anal. Real World Appl., 37, 329-349, 2017 link 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