Space-time spectral element method for solution of second-order hyperbolic equations. (English) Zbl 0831.65104
A two-field mixed-hybrid spectral element formulation in time and space is presented for solution of a second-order scalar hyperbolic equation. Explicit and implicit algorithms are developed and used to solve this equation.
The algorithms are analyzed and their characteristics are presented in terms of truncation error and stability. This analysis is confirmed by numerical results. The improvement in accuracy in comparison with semi- discrete schemes is indicated.
The algorithms are analyzed and their characteristics are presented in terms of truncation error and stability. This analysis is confirmed by numerical results. The improvement in accuracy in comparison with semi- discrete schemes is indicated.
Reviewer: Z.Dżygadło (Warszawa)
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35L70 | Second-order nonlinear hyperbolic equations |
Keywords:
mixed-hybrid spectral element formulation; second-order scalar hyperbolic equation; truncation error; stability; numerical resultsReferences:
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