Global and local radial basis function collocation methods for solving convection-diffusion equations Métodos de colocación de función de base globales y locales radiales para solucionar ecuaciones de difusión de convección

In order to assess the performance of some meshless methods based on Radial Basis Function (RBF) Collocation, it is presented a comprehensive comparison between global and multi-domain formulations for solving convection-diffusion equations. Global formulations included are the symmetric or Fasshauer’s method and the overlapping two-domain decomposition method (the classical additive Schwarz technique) incorporating the symmetric approach. Two local or multi-domain (molecules) formulations included are approaches with and without the use of PDE-information. The new local formulation with PDE-information, it is achieved by the inclusion of the partial differential equation (PDE) operator into a local Hermite RBF interpolation in analogy to Fasshauer’s method at the advantages improved stability and fast computation. In addition, an enhanced way for introducing the local convection velocity field is achieved which approximates required derivatives of governing equations used in a point collocation technique on centrally defined computational molecules. It is showed that this approach yielded to more accurate solutions and free of so-called spurious oscillations that features the numerical solution of convective dominated problems.