EXPONENTIAL TIME DIFFERENCING-PADE FINITE ELEMENT METHOD FOR NONLINEAR CONVECTION-DIFFUSION-REACTION EQUATIONS WITH TIME CONSTANT DELAY  

作　　者：Haishen Dai Qiumei Huang Cheng Wang 

机构地区：[1]School of Mathematics,Faculty of Science,Beijing University of Technology,Beijing 100124,China [2]Department of Mathematics,University of Massachusetts,North Dartmouth,MA 02747,USA

出　　处：《Journal of Computational Mathematics》2023年第3期370-394,共25页计算数学（英文）

基　　金：NSFC 11971047(Q.Huang)and NSF DMS-2012669(C.Wang).

摘　　要：In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions.An ETD-based RK is used for time integration of the corresponding equation.To overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator,the Padéapproach is used for such an exponential operator approximation,which in turn leads to the corresponding ETD-Padéschemes.An unconditional L^(2) numerical stability is proved for the proposed numerical schemes,under a global Lipshitz continuity assumption.In addition,optimal rate error estimates are provided,which gives the convergence order of O(k^(3)+h^(r))(ETD3-Padé)or O(k^(4)+h^(r))(ETD4-Padé)in the L^(2)norm,respectively.Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.

关 键 词：Nonlinear delayed convection diffusion reaction equations ETD-Pad´e scheme Lipshitz continuity L^(2)stability analysis Convergence analysis and error estimate 

分 类 号：O17[理学—数学]