Abstract
AbstractA methodology for analysing the numerical errors generated by schemes using high‐order approximation is presented. Based on Fourier analysis, this methodology is illustrated through the study of the θ‐weighting Taylor–Galerkin finite element model applied to an unsteady one‐dimension 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. Moreover, it appears 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. Numerical tests are presented to support the validity of the proposed strategy. We recommend strongly the use of this method for studying the behaviour of numerical schemes based on high‐order approximations.
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