term;
Fully implicit finite element scheme;
Two-layer coupled discretization;
Second-order time accuracy;
Existence;
Convergence;
Diffusion problem with nonlinear capacity;
NONEQUILIBRIUM RADIATION DIFFUSION;
GALERKIN APPROXIMATIONS;
PARABOLIC EQUATIONS;
ERROR ANALYSIS;
CONVERGENCE;
ITERATION;
ACCURACY;
D O I:
10.1016/j.cam.2023.115512
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
A new nonlinear finite element method is studied to solve multi-dimensional anisotropic nonlinear diffusion equation with nonlinear capacity term, especially to secure a vivid simulation in the case of problems with transient physical quantities. In the scheme design, fully implicit two-layer coupled discretization is applied to assure high time accuracy, and finite element discretization is applied to assure high space accuracy. By introducing Ritz projection and new inductive reasoning methods, we develop the discrete functional analysis technique from that for finite difference schemes, and establish a new general analysis framework for nonlinear finite element schemes. Consequently, we overcome the difficulties arising from the strong coupling of the nonlinear finite element discretizations for the capacity term and diffusion operator, and prove the existence and boundedness of the nonlinear finite element solution, as well as its second-order time and optimal order space convergence. Numerical experiments and comparisons confirm the theoretical analysis results and demonstrate its high performance.& COPY; 2023 Elsevier B.V. All rights reserved.
机构:
Inst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R ChinaInst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R China
Cui, Xia
Yuan, Guangwei
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h-index: 0
机构:
Inst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R ChinaInst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R China
Yuan, Guangwei
Zhao, Fei
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h-index: 0
机构:
North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R ChinaInst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R China
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
Feng, Xinlong
He, Yinnian
论文数: 0引用数: 0
h-index: 0
机构:
Xi An Jiao Tong Univ, Ctr Computat Geosci, Sch Math & Stat, Xian 710049, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
机构:
Inst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R ChinaInst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R China
Cui, Xia
Yuan, Guangwei
论文数: 0引用数: 0
h-index: 0
机构:
Inst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R ChinaInst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R China
Yuan, Guangwei
Zhao, Fei
论文数: 0引用数: 0
h-index: 0
机构:
North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R ChinaInst Appl Phys & Computat Math, Lab Computat Phys, POB 8009-26, Beijing 100088, Peoples R China
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
Feng, Xinlong
He, Yinnian
论文数: 0引用数: 0
h-index: 0
机构:
Xi An Jiao Tong Univ, Ctr Computat Geosci, Sch Math & Stat, Xian 710049, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China