Convergence of FEM with interpolated coefficients for semilinear hyperbolic equation

Journal of Computational and Applied Mathematics

Volumn 214, Issue 1, 2008, Pages 313-317

  Xiong, Zhiguang ^a,b   Chen, Yanping ^b   Zhang, Yan ^b  

^a HUNAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b XIANGTAN UNIVERSITY   (China)

Author keywords

Convergence; Finite element with interpolated coefficients; Semilinear hyperbolic equations

Indexed keywords

APPROXIMATION ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; NONLINEAR ANALYSIS; PROBLEM SOLVING;

INTERPOLATED COEFFICIENTS; SEMILINEAR HYPERBOLIC EQUATIONS;

FINITE ELEMENT METHOD;

EID: 38949213391     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.02.023     Document Type: Article

References (16)

1. Baker G.A., Dougalis V.A., and Karakashian O. On multistep-Galerkin discretizations of semilinear hyperbolic and parabolic equations. Nonlinear Anal. 4 (1980) 579-597
2. Bales L.A. Semidiscrete and single step fully discrete approximations for second order hyperbolic equations with time-dependent coefficients. Math. Comp. 43 (1984) 383-414
3. Bales L.A. Higher order single step fully discrete approximations for second hyperbolic equations with time dependent coefficients. SIAM J. Numer. Anal. 23 (1986) 27-43
4. Bales L.A. Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations, Hyperbolic partial differential equations V. Comput. Math. Appl. 15 (1988) 535-553
5. Bales L.A., and Dougalis V.A. Cosine methods for nonlinear second-order hyperbolic equations. Math. Comp. 52 (1989) 299-319
6. Bramble J.H. A second-order finite difference analog of the first biharmonia boundary value problem. Numer. Math. 9 4 (1966) 236-249
7. Chen C.M. Structure theory of superconvergence of finite elements (2001), Hunan Press of Science and Technology, Changsha (in Chinese)
8. Chen C.M., Larson S., and Zhang N.Y. Error estimates of optimal order for finite element methods interpolated coefficients for the nonlinear heat equation. IMA J. Numer. Anal. 9 (1989) 507-524
9. Larson S., Tomee V., and Zhang N.Y. Interpolation of coefficients and transformation of dependent variable in element methods for the nonlinear heat equation. Math. Methods Appl. Sci. 11 (1989) 105-124
10. Lei D., and Chen C.M. Superconvergence for finite element method with interpolated coefficients for nonlinear elliptic problem. Natur. Sci. J. Xiangtan Univ. 22 (2000) 15-19 (in Chinese)
11. Lin Q., Wang H., and Lin T. Interpolated FEM for second order hyperbolic equations and their global superconvergence. Systems Sci. Math. Sci. 4 (1993) 331-340
12. Wang H. Superconvergence of full-discrete finite element solution and its derivative for a class of quasilinear hyperbolic equations. Northeast. Math. J. 2 (1986) 205-214
13. Xiong Z.G., and Chen C.M. Superconvergence of triangular quadratic finite element method with interpolated coefficients for nonlinear elliptic problem. Acta Math. Sci. Ser. A 26 (2006) 174-182 (in Chinese)
14. Xiong Z.G., and Chen C.M. Superconvergence of rectangular finite element with interpolated coefficients for semilinear elliptic problem. Appl. Math. Comput. 181 (2006) 1577-1584
15. Xiong Z.G., and Hu H. Simplified continuous finite element method for a class of nonlinear oscillating equations. J. Sound Vib. 287 (2005) 367-373
16. Zlamal M. A finite element solution of the nonlinear heat equation. RAIRO Anal. Numer. 14 (1980) 203-216