A Finite Element enrichment technique by the Meshless Local Petrov-Galerkin method

In the engineering practice meshing and re-meshing complex domains by Finite Elements (FE) is one of the most time-consuming efforts. Meshless methods avoid this task but are computationally more expensive than standard FE. A somewhat natural improvement can be attempted by combining the two techniques with the aim at emphasizing the respective merits. The present work describes a FE enrichment by the Meshless Local Petrov-Galerkin (MLPG) method. The basic idea is to add a limited number of moving MLPG points over a fixed coarse FE grid, in order to improve the solution accuracy in specific regions of the domain with no mesh refinements. The transient Poisson equation is used as a test problem, with the numerical convergence of the enriched FE-MLPG method verified in several cases. The enriched approach proves more accurate than standard FE even by a factor 15 with a small number of MLPG nodes added.