Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (6): 1179-1190.
• Articles • Previous Articles Next Articles
HE Siriguleng, LI Hong
Received:
2011-07-18
Revised:
2012-05-18
Online:
2012-12-25
Published:
2012-12-25
Supported by:
国家自然科学基金(11061021)、内蒙古自治区高等学校科学研究项目(NJ10006)、内蒙古大学研究生培养基金和内蒙古自然科学基金(2012MS0106)资助
CLC Number:
HE Siriguleng, LI Hong. Mixed Space--time Discontinuous Galerkin Method for Elastodynamics[J].Acta mathematica scientia,Series A, 2012, 32(6): 1179-1190.
[1] Hughes T J R, Hulbert G M. Space--time finite element methods for elastodynamics: formulations and error estimates. Comput Methods Appl Mech Engrg, 1988, 66(3): 339--363 [2] Hulbert G M, Hughes T J R. Space--time finite element methods for second--order hyperbolic equations. Comput Methods Appl Mech Engrg, 1990, 84: 327--348 [3] Hulbert G M. The finite element methods for structural dynamics. Int J Numer Methods Engrg, 1992, 33: 307--331 [4] Johnson C. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Comput Methods Appl Mech Engrg, [5] Thomée V. Galerkin Finite Element Methods for Parabolic Problems. New York: Springer--Verlag, 1997 [6] Karakashian O, Makridakis Ch. A space--time finite element method for the nonlinear Schr\"{o}dinger equation: the discontinuous Galerkin method. Math Comput, 1998, 67: 479--499 [7] Li H, Liu R X. The space--time finite element methods for parabolic problems. Appl Math Mech, 2001, 22: 687--700 [8] 李宏. 非线性抛物方程的时空有限元法的误差估计. 高等学校计算数学学报, 2005, 27(1): 34--45 [9] 李宏, 王焕清. 半线性抛物型积分微分方程的间断时空有限元法. 计算数学, 2006, 28(3): 293--308 [10] 何斯日古楞, 李宏. 带广义边界条件的四阶抛物型方程的混合间断时空有限元法. 计算数学, 2009, 31(2): 167--178 [11] Sun T, Ma K. A space--time discontinuous Galerkin method for linear convection-dominated Sobolev equations. Appl Math Comput, [12] French D A. A space--time finite element method for the wave equation. Comput Methods Appl Mech Engrg, 1993, 107: 145--157 [13] 应隆安, 陈传淼. 有限元理论与方法(第二分册). 北京: 科学出版社, 2009 [14] Chien C C, Yang C S, Tang J H. Three--dimensional transient elastodynamic analysis by a space and time discontinuous Galerkin finite element method. Finite Elem Anal Des, 2003, 39: 561--580 [15] 于开平, 邹经湘. 时域有限元法. 力学进展, 1998, 28(4): 461--468 [16] Kunthong P, Thompson L L. An efficient solver for the high--order accurate time-discontinuous Galerkin (TDG) method for second-order hyperbolic systems. Finite Elem Anal Des, 2005, 41: 729--762 [17] Li X D, Wiberg N E. Structural dynamic analysis by a time--discontinuous Galerkin finite element method. Int J Numer Methods Engrg, 1996, 39: 2131--2152 [18] Li X, Yao D. Time discontinuous Galerkin finite element method for dynamic analysis in saturated poro--elasto--plastic medium. [19] Dautray R, Lious I. Evolution Problems I, Mathematical Analysis and Numerical Methods for Science and Technology, Vol 5. Berlin: Springer, 1988 [20] Evans L C. Partial Differential Equations. Providence, RI: AMS Press, 1999 [21] Hughes T J R, Marsden J E. Classical elastodyanmics as a linear symmetric hyperbolic system. Journal of Elasticity, 1978, 8: 97--110 [22] Brenner S C, Scott L R. The Mathematical Theory of Finite Element Methods. New York: Springer-Verlag, 2002 |
[1] | Gu Haibo, Gao Caixia. Razumikhin-Type Theorems on P-th Moment and Almost Sure Stability of Neutral Stochastic Switched Nonlinear Systems [J]. Acta mathematica scientia,Series A, 2018, 38(5): 970-983. |
[2] | Zheng Lifei, Guo Jie, Wu Meihua, Wang Xiaorui, Wan Aying. The Research on a Class of the Predator-Prey-Mutualist System with Delays [J]. Acta mathematica scientia,Series A, 2018, 38(5): 1001-1013. |
[3] | Wu Bin, Gao Ying, Yan Lin, Yu Jun. Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem [J]. Acta mathematica scientia,Series A, 2018, 38(4): 779-799. |
[4] | Wang Junli, Zhang Xingwei, Liu Jian. Instability of Plane Couette-Poiseuille Flow of Compressible Navier-Stokes Equation [J]. Acta mathematica scientia,Series A, 2018, 38(2): 322-333. |
[5] | Fang Zhichao, Li Hong, Luo Zhendong, Liu Yang. Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation [J]. Acta mathematica scientia,Series A, 2018, 38(2): 395-416. |
[6] | Wang Wansheng, Zhong Peng, Zhao Xinyang. Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay [J]. Acta mathematica scientia,Series A, 2018, 38(1): 96-109. |
[7] | Li Haixia. Stability and Uniqueness of Positive Solutions for a Food-Chain Model [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1094-1104. |
[8] | Meng Xiaoying. Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1162-1175. |
[9] | Wang Chun, Xu Tianzhou. Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(5): 846-859. |
[10] | Chen Hongbin, Gan Siqing, Xu Da, Peng Yulong. A Formally Second-Order BDF Compact ADI Difference Scheme for the Two-Dimensional Fractional Evolution Equation [J]. Acta mathematica scientia,Series A, 2017, 37(5): 976-992. |
[11] | Yang Jihua, Zhang Erli, Liu Mei. Dynamic Analysis and Chaos Control of a Finance System with Delayed Feedbacks [J]. Acta mathematica scientia,Series A, 2017, 37(4): 767-782. |
[12] | Xiong Jun, Li Junmin, He Chao. Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs [J]. Acta mathematica scientia,Series A, 2017, 37(3): 469-477. |
[13] | Wei Aiju, Zhang Xinjian, Wang Junyi, Li Kezan. Dynamics Analysis of an Ebola Epidemic Model [J]. Acta mathematica scientia,Series A, 2017, 37(3): 577-592. |
[14] | Wang Wei, Zhu Yucan. Stability of Fusion Frame Systems under Perturbation of the Local Frame Vectors [J]. Acta mathematica scientia,Series A, 2017, 37(2): 228-238. |
[15] | Wang Xuewu. Convergence and Stability of Ishikawa Type Iterative Sequences for the φ-Hemi Pseudocontractive Operator Pair [J]. Acta mathematica scientia,Series A, 2017, 37(2): 248-256. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||||||
Full text 22
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Abstract 102
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Shared | ||||||||||||||||||||||||||||||||||||||||||||||||||
Discussed |
|