Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations

被引：3
作者：
Cui, Ming [1 ]
Li, Yanfei [1 ]
Yao, Changhui [2 ]
机构：
[1] Beijing Univ Technol, Fac Sci, Beijing 1000124, Peoples R China
[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2023年 / 15卷 / 03期
基金：
中国国家自然科学基金; 北京市自然科学基金;
关键词：
Energy conserving; the nonlinear coupled Klein-Gordon equations; unconditional superconvergence result; postprocessing interpolation; finite element method; WAVE-PROPAGATION; CONVERGENCE; SCHEME; APPROXIMATION; MODEL; TANH; FLOW; FEM;
D O I：
10.4208/aamm.OA-2021-0261
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the energy conserving numerical scheme for cou-pled nonlinear Klein-Gordon equations. We propose energy conserving finite element method and get the unconditional superconvergence result O(h2+Delta t2) by using the er-ror splitting technique and postprocessing interpolation. Numerical experiments are carried out to support our theoretical results.
引用
收藏
页码：602 / 622
页数：21
相关论文
共 48 条
[1]   HIGH ORDER ASYMPTOTIC PRESERVING DEFERRED CORRECTION IMPLICIT-EXPLICIT SCHEMES FOR KINETIC MODELS [J].
Abgrall, Remi ;
Torlo, Davide .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (03) :B816-B845
[2]  
[Anonymous], 1965, P S APPL MATH
[3]   Regularized numerical methods for the logarithmic Schrodinger equation [J].
Bao, Weizhu ;
Carles, Remi ;
Su, Chunmei ;
Tang, Qinglin .
NUMERISCHE MATHEMATIK, 2019, 143 (02) :461-487
[4]   CONVERGENCE ANALYSIS OF A SECOND ORDER CONVEX SPLITTING SCHEME FOR THE MODIFIED PHASE FIELD CRYSTAL EQUATION [J].
Baskaran, A. ;
Lowengrub, J. S. ;
Wang, C. ;
Wise, S. M. .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (05) :2851-2873
[5]   Existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the de Sitter-Kerr-Newman metric [J].
Besset, Nicolas ;
Hafner, Dietrich .
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2021, 18 (02) :293-310
[6]  
Biswas A, 2014, P ROMANIAN ACAD A, V15, P123
[7]   Nonlinear dynamics of the Frenkel-Kontorova model [J].
Braun, OM ;
Kivshar, YS .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1998, 306 (1-2) :1-108
[8]   Spherical interface dynamos: Mathematical theory, finite element approximation, and application [J].
Chan, Kit Hung ;
Zhang, Keke ;
Zou, Jun .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (05) :1877-1902
[9]   A Fourier Pseudospectral Method for the "Good" Boussinesq Equation with Second-Order Temporal Accuracy [J].
Cheng, Kelong ;
Feng, Wenqiang ;
Gottlieb, Sigal ;
Wang, Cheng .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2015, 31 (01) :202-224
[10]   An Efficient and Unconditionally Convergent Galerkin inite Element Method for the Nonlinear Schrodinger Equation in High Dimensions [J].
Cheng, Yue ;
Wang, Tingchun ;
Guo, Boling .
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 13 (04) :735-760
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