Academic Journal
Superconvergence analysis of an energy-preserving Galerkin method for a class of nonlinear wave equation.
| Τίτλος: | Superconvergence analysis of an energy-preserving Galerkin method for a class of nonlinear wave equation. |
|---|---|
| Συγγραφείς: | Liao, Xin1 (AUTHOR), Wang, Lele1 (AUTHOR) wanglele@zua.edu.cn, Yang, Huaijun1 (AUTHOR) |
| Πηγή: | Computers & Mathematics with Applications. Oct2026, Vol. 219, p150-162. 13p. |
| Θεματικοί όροι: | *Galerkin methods, *Nonlinear wave equations, *Energy conservation, *Time integration scheme, *Numerical analysis, *Approximation error, *Finite element method |
| Περίληψη: | In this paper, the superconvergence analysis of an energy-preserving Galerkin approximation scheme, which is based upon the low-order bilinear finite element method in space and a second-order time-stepping scheme in time, is developed and investigated for a class of nonlinear wave equation without the global Lipschitz continuity requirement of the nonlinear term. More precisely, an equivalent system is introduced firstly in terms of the methods of order reduction in time. Then the energy conservation is proved and a uniform boundedness of the numerical solution in energy norm is obtained skillfully. Furthermore, the superclose error estimates are derived rigorously with the aid of the high-accuracy estimate of the bilinear element. Subsequently, the global superconvergence error estimates are acquired by interpolation post-processing approach. Finally, some numerical experiments are carried out to confirm the theoretical findings. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
καταχωρήστε σχόλιο πρώτοι!