Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
3.4 The Moving Least-Squares (MLS) Smoothing Scheme
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Despite the efforts in optimizing the shape parameter, c, of the RBF expansion for every topology, it is found that derivative fields, in particular odd one-sided derivatives, such as those found in convective terms of transport equations as well as in divergence operators, tend to oscillate specially towards the areas of large gradients such as re-circulating zones, corners, impingement planes, etc. For this reason, additional care must be taken when formulating the direct derivative expansion vectors within each topology.