Analysis of time varying errors in quadratic finite element approximation of hyperbolic problems. (English) Zbl 0854.65076
A methodology leading to an adequate computation of the dissipation and dispersion errors is presented when high-order approximation is considered. Based on Fourier analysis, this methodology is illustrated through the study of the \(\theta\)-weighting Taylor-Galerkin finite element model applied to an unsteady one-dimensional advection problem with quadratic elements. Results show that the dissipation and dispersion errors may be computed by considering simultaneously the so-called physical and computational modes and then, contrarily to what is shown when linear approximation is considered, these errors present a transient behaviour.
It is shown by numerical experiments, that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another. A comparison between the computed values using the so-called model and the predicted values from the error analysis shows clearly the validity of the proposed error analysis methodology.
It is shown by numerical experiments, that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another. A comparison between the computed values using the so-called model and the predicted values from the error analysis shows clearly the validity of the proposed error analysis methodology.
Reviewer: K.Zlateva (Russe)
MSC:
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
Keywords:
hyperbolic problems; dissipation error; dispersion errors; Taylor-Galerkin finite element model; advection problem; quadratic elements; numerical experimentsReferences:
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