Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems

被引:4
作者
Yi, Huaming [1 ]
Chen, Yanping [2 ]
Wang, Yang [3 ]
Huang, Yunqing [1 ]
机构
[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
[3] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Peoples R China
基金
中国国家自然科学基金;
关键词
Convergence analysis; Backward difference formula; Time -discrete system; Immersed finite element; Parabolic interface problem; FINITE-ELEMENT-METHOD; ELECTROMAGNETIC-WAVES; ERROR ANALYSIS; POROUS-MEDIA; FEM; APPROXIMATION; EQUATIONS; FLOW;
D O I
10.1016/j.amc.2022.127581
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The article proposes and analyzes the optimal error estimates of a second-order backward difference formula (BDF2) numerical scheme for the semi-linear parabolic interface prob-lems. The partially penalized immersed finite element (PPIFE) methods are used for the spatial discretization to resolve discontinuity of the diffusion coefficient across the inter-face. The classical extrapolation method is adopted to treat the nonlinear term, which ef-fectively avoids the complicated numerical calculation of the nonlinearity. Our error anal-ysis is based on the corresponding time-discrete system, which neatly splits the error into two parts: the temporal discretization error and the spatial discretization error. Since the spatial discretization error is independent of time step size Tau, we can unconditionally de-rive the optimal error estimates in both L 2 norm and semi -H 1 norm, while previous works always require the coupling condition of time step and space size. Numerical experiments are given to confirm the theoretical analysis.(c) 2022 Elsevier Inc. All rights reserved.
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页数:20
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