孟雄 - 哈尔滨工业大学

个人简介

孟雄，男，1985年9月生于安徽固镇，哈尔滨工业大学数学学院教授、博导、省优青，欧盟玛丽居里学者、美国布朗大学访问学者，主要研究方向为对流占优偏微分方程的高阶精度数值方法，尤其是间断有限元方法的设计、分析与应用。在SIAM Journal on Numerical Analysis, Numerische Mathematik, Mathematics of Computation, IMA Journal of Numerical Analysis等计算数学期刊发表论文17篇。主持欧盟“玛丽居里行动”计划基金、国家自然科学基金面上项目、国家自然科学基金青年基金等项目。获中国工业与应用数学学会应用数学青年科技奖、国家天元数学东北中心优秀青年学者等奖励。工作经历 2021.12 – 至今：哈尔滨工业大学数学学院教授（准聘） 2019.09 – 2020.07：美国布朗大学应用数学系访问学者（合作导师 Chi-Wang Shu 教授） 2015.12 – 2021.12：哈尔滨工业大学数学学院副教授（校青年拔尖） 2014.09 – 2016.08：英国东安格利亚大学数学学院玛丽居里学者（合作导师 Jennifer Ryan 教授） 2013.10 – 2015.12：哈尔滨工业大学数学学院讲师教育经历 2010.08 – 2012.08：美国布朗大学应用数学系联合培养（联合导师 Chi-Wang Shu 教授） 2008.09 – 2013.10：哈尔滨工业大学数学学院博士（导师吴勃英教授） 2004.09 – 2008.07：哈尔滨工业大学数学学院学士荣誉称号应用数学青年科技奖，中国工业与应用数学学会，2022 天元优秀青年学者，国家天元数学东北中心，2021 省优秀青年基金，黑龙江省科学技术厅，2021 省优秀青年学术奖，黑龙江省数学会，2021 省自然科学三等奖，黑龙江省人民政府，2018 校优秀博士学位论文，哈尔滨工业大学，2015 欧盟玛丽居里学者，欧盟，2014

研究领域

计算流体力学的高阶精度数值方法，尤其是间断有限元方法的设计、分析与应用间断有限元方法的超收敛性研究，包括超逼近性质和负模误差估计与后处理理论等广义数值流通量间断有限元方法的构造与应用

近期论文

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Hongjuan Zhang, Xiong Meng*, Dazhi Zhang, and Boying Wu, Optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional KdV type equations, Journal of Computational Mathematics, 2023, to appear. Hongjuan Zhang, Boying Wu, and Xiong Meng*, Analysis of the local discontinuous Galerkin method with generalized fluxes for one-dimensional nonlinear convection-diffusion systems, Science China Mathematics, 2023, to appear, DOI: 10.1007/s11425-022-2035-y. Hongjuan Zhang, Boying Wu, and Xiong Meng*, A local discontinuous Galerkin method with generalized alternating fluxes for 2D nonlinear Schrodinger equations, Communications on Applied Mathematics and Computation, 2022, 4(1): 84–107. paper.pdf Xiaobin Liu, Dazhi Zhang, Xiong Meng*, and Boying Wu, Superconvergence of the local discontinuous Galerkin method for one dimensional nonlinear convection-diffusion equations, Journal of Scientific Computing, 2021, 87(1): article 39.paper.pdf Xiaobin Liu, Dazhi Zhang, Xiong Meng*, and Boying Wu, Superconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations, Science China Mathematics, 2021, 64(6): 1305–1320. paper.pdf Yuan Xu, Xiong Meng, Chi-Wang Shu, and Qiang Zhang*, Superconvergence analysis of the Runge-Kutta discontinuous Galerkin methods for a linear hyperbolic equation, Journal of Scientific Computing, 2020, 84(1): article 23. paper.pdf Minghui Liu, Boying Wu, and Xiong Meng*, Optimal error estimates of the discontinuous Galerkin method with upwind-biased fluxes for 2D linear variable coefficients hyperbolic equations, Journal of Scientific Computing, 2020, 83(1): article 9. paper.pdf Jia Li, Dazhi Zhang, Xiong Meng*, Boying Wu, and Qiang Zhang, Discontinuous Galerkin methods for nonlinear scalar conservation laws: generalized local Lax–Friedrichs numerical fluxes, SIAM Journal on Numerical Analysis, 2020, 58(1): 1–20. paper.pdf Jia Li, Dazhi Zhang, Xiong Meng*, and Boying Wu, Analysis of local discontinuous Galerkin methods with generalized numerical fluxes for linearized KdV equations, Mathematics of Computation, 2020, 89(325): 2085–2111. paper.pdf Jia Li, Dazhi Zhang, Xiong Meng*, and Boying Wu, Analysis of discontinuous Galerkin methods with upwind-biased fluxes for one dimensional linear hyperbolic equations with degenerate variable coefficients, Journal of Scientific Computing, 2019, 78(3): 1305–1328. paper.pdf Xiong Meng, and Jennifer K. Ryan*, Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation laws, IMA Journal of Numerical Analysis, 2018, 38(1): 125–155. paper.pdf Xiong Meng, and Jennifer K. Ryan*, Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement, Numerische Mathematik, 2017, 136(1): 27–73. paper.pdf Yao Cheng, Xiong Meng, and Qiang Zhang*, Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations, Mathematics of Computation, 2017, 86(305): 1233–1267. paper.pdf Xiong Meng, Chi-Wang Shu*, and Boying Wu, Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations, Mathematics of Computation, 2016, 85(299): 1225–1261. paper.pdf 孟雄, 舒其望*, 杨扬, 发展型偏微分方程间断有限元方法的超收敛性, 中国科学: 数学, 2015, 45(7): 1041–1060. paper.pdf Xiong Meng*, Chi-Wang Shu, Qiang Zhang and Boying Wu, Superconvergence of discontinuous Galerkin methods for scalar nonlinear conservation laws in one space dimension, SIAM Journal on Numerical Analysis, 2012, 50(5): 2336–2356. paper.pdf Xiong Meng*, Chi-Wang Shu, and Boying Wu, Superconvergence of the local discontinuous Galerkin method for linear fourth-order time-dependent problems in one space dimension, IMA Journal of Numerical Analysis, 2012, 32(4): 1294–1328. paper.pdf

学术兼职

中国数学会计算数学分会理事教育部第五轮学科评估通讯评审专家国家自然科学基金通讯评审专家美国《数学评论》评论员教育部学位与研究生教育发展中心通讯评审专家