Meshless techniques for anisotropic diffusion

Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations. They have been successfully used for solving many real-life problems. Their efficiency is downgraded by the requirement of performing numerical multi-dimensional integration of tricky, non-polynomial factors. Recently, Direct MLPG (DMLPG) methods have been proposed. DMLPG techniques require lower computational costs with respect to their MLPG counterparts. The DMLPG accuracy has been initially analyzed in few papers, but its performance is quite unexplored. In this paper, we perform numerical comparisons between MLPG and DMLPG accuracy and efficiency in solving anisotropic diffusion problems. In particular, we set different boundary conditions, in order to check if and when MLPG and/or DMLPG suffer locking effects.