One-dimensional finite element grids based on a localized truncation erroranalysis

With the exponential increase in computing power, modelers of coastal and o ceanic regions are capable of simulating larger domains with increased reso lution. Typically, these models use graded meshes wherein the size of the e lements can vary by orders of magnitude. However, with notably few exceptio ns, the graded meshes are generated using criteria that neither optimize pl acement of the node points nor properly incorporate the physics, as represe nted by discrete equations, underlying tidal flow and circulation to the me sh generation process. Consequently, the user of the model must heuristical ly adjust such meshes based on knowledge of local flow and topographical fe atures--a rough and time consuming proposition at best. Herein, a localized truncation error analysis (LTEA) is proposed as a means to efficiently gen erate meshes that incorporate estimates of flow variables and their derivat ives. In a one-dimensional (1D) setting, three different LTEA-based finite element grid generation methodologies are examined and compared with two co mmon algorithms: the wavelength to Delta x ratio criterion and the topograp hical length scale criterion. Errors are compared on a per node basis. It i s shown that solutions based on LTEA meshes are, in general, more accurate (both locally and globally) and more efficient. In addition, the study show s that the first four terms of the ordered truncation error series are in d irect competition and, subsequently, that the leading order term of the tru ncation error series is not necessarily the dominant term. Analyses and res ults from this 1D study lay the groundwork for developing an efficient mesh generating algorithm suitable for two-dimensional (2D) models. Copyright ( C) 2000 John Wiley & Sons, Ltd.