DISCRETE ENERGY ANALYSIS OF THE THIRD-ORDER VARIABLE-STEP BDF TIME-STEPPING FOR DIFFUSION EQUATIONS  

作　　者：Hong-lin Liao Tao Tang Tao Zhou 

机构地区：[1]Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China [2]Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106,China [3]Division of Science and Technology,BNU-HKBU United International College,Zhuhai 519087,China [4]Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China

出　　处：《Journal of Computational Mathematics》2023年第2期325-344,共20页计算数学（英文）

基　　金：supported by NSF of China under grant number 12071216;supported by NNW2018-ZT4A06 project;supported by NSF of China under grant numbers 12288201;youth innovation promotion association(CAS).

摘　　要：This is one of our series works on discrete energy analysis of the variable-step BDF schemes.In this part,we present stability and convergence analysis of the third-order BDF(BDF3)schemes with variable steps for linear diffusion equations,see,e.g.,[SIAM J.Numer.Anal.,58:2294-2314]and[Math.Comp.,90:1207-1226]for our previous works on the BDF2 scheme.To this aim,we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877,by which we can establish a discrete energy dissipation law.Mesh-robust stability and convergence analysis in the L^(2) norm are then obtained.Here the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step ratios.We also present numerical tests to support our theoretical results.

关 键 词：Diffusion equations Variable-step third-order BDF scheme Discrete gradient structure Discrete orthogonal convolution kernels Stability and convergence 

分 类 号：O175[理学—数学]