In this talk, we  present a local discontinuous Galerkin (LDG) method for nonlinear time-dependent equations, whose element-based discretization benefits adaptivity, parallel computing, and high-order accuracy on unstructured meshes. A novel semi-implicit time marching method is developed for highly nonlinear ODEs without easily separable stiff and non-stiff components. Combined with LDG discretization, the fully discrete schemes achieve high-order accuracy in space and time with stable time steps proportional to the mesh size. Furthermore, structure preserving limiters are coupled to implicit DG discretizations via Lagrange multipliers, yielding a KKT formulation solved by an active set semi-smooth Newton method with proven convergence. Numerical experiments demonstrate the accuracy and capability of the proposed method.

中国科学技术大学数学学院教授、博士生导师。主要从事间断有限元方法的研究工作，发表高水平科研论文80余篇。近年来徐岩教授承担国家自然科学基金、中科院、教育部基金、霍英东基金等多相科学基金项目的研究。先后获得教育部新世纪优秀人才支持计划(2009) 、中国科学院/全国博士学位论文奖(2007, 2008)、中国科学技术大学优秀青年教师奖(2010, 2013, 2016) 、优秀研究生指导教师奖(2013,2016)、中国数学会计算数学学会青年创新奖(2016)、国家自然科学基金委优秀青年基金(2017)，入选国家高层次人才。担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation等杂志的编委。