文献类型：期刊文献

英文题名：Direct discontinuous Galerkin method for solving nonlinear time fractional diffusion equation with weak singularity solution

作者：Ren, Jincheng[1];Huang, Chaobao[2];An, Na[3]

通讯作者：Huang, CB[1]

机构：[1]Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450045, Peoples R China;[2]Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China;[3]Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China.

年份：2020

卷号：102

外文期刊名：APPLIED MATHEMATICS LETTERS

收录：;EI(收录号：20194507634212);Scopus(收录号：2-s2.0-85074407305);WOS:【SCI-EXPANDED(收录号:WOS:000514015000026)】；

基金：The research is supported by the National Natural Science Foundation of China (Nos. 11601119 and 11801332), Sponsored by Program for HASTIT, China (No.18HASTIT027) and Young talents Fund of HUEL, China.

语种：英文

外文关键词：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.