标题：Direct discontinuous Galerkin method for solving nonlinear time fractional diffusion equation with weak singularity solution
作者：Ren, Jincheng; Huang, Chaobao; An, Na
作者机构：[Ren, Jincheng] Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450045, Peoples R China.; [Huang, Chaobao] Shandong Univ Finance & Econ, 更多
通讯作者：Huang, Chaobao;Huang, CB
通讯作者地址：[Huang, CB]Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China.
来源：APPLIED MATHEMATICS LETTERS
关键词：Nonlinear time fractional diffusion equation; DDG method; The L1; formula; Graded mesh; Optimal error estimate
摘要：In this work, the nonlinear time fractional diffusion equation with Caputo fractional derivative of order alpha is an element of (0, 1) is considered. By the well-known L1-type formula of Caputo derivative on a graded mesh in time, a direct discontinuous Galerkin (DDG) method on a uniform mesh in space, and the Newton linearization method approximation of the nonlinear term, a fully discrete DDG scheme is constructed. Its error at each time level t(n) is bounded in the L-2(Omega) norm by means of a non-trivial projection of an unknown solution into the finite element space. Then, the optimal error estimate is proved by choosing a suitable graded mesh. Numerical experiments are presented to verify that our analysis is sharp. (C) 2019 Elsevier Ltd. All rights reserved.