报告题目 (Title)：非线性Caputo分数阶微分方程的hp间断Galerkin方法的指数收敛

报告人 (Speaker)： 陈艳萍 教授（华南师范大学）

报告时间 (Time)：2022年6月17日 (周五) 16:00

报告地点 (Place)：腾讯会议（会议号：598-109-288）

邀请人(Inviter)：刘东杰

主办部门：理学院数学系

报告摘要：

We present an hp-discontinuous Galerkin method for solving nonlinear fractional differential equations involving Caputo-type fractional derivative. The main idea behind our approach is to first transform the fractional differential equations into nonlinear Volterra or Fredholm integral equations, and then the hp-discontinuous Galerkin method is used to solve the equivalent integral equations. We derive a-priori error bounds in the L2 -norm that are totally explicit with respect to the local mesh sizes, the local polynomial degrees, and the local regularities of the exact solutions. In particular, we prove that exponential convergence can be achieved for solutions with endpoint singularities by using geometrically refined meshes and linearly increasing approximation orders. The theoretical results are confirmed by a series of numerical experiments.