A coupled finite element and meshless local Petrov–Galerkin method for two-dimensional potential problems Original Research Article

A coupled finite element (FE) and meshless local Petrov–Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. A transition region is created between the FE and MLPG regions. The transition region blends the trial and test functions of the FE and MLPG regions. The trial function blending is achieved using a new coupling technique similar to the ‘Coons patch’ method that is widely used in computer aided geometric design. By using the technique, trial functions, which are similar to the isoparametric “serendipity” element, of the transition element can be constructed. The test function blending is achieved by using either the FE or MLPG test functions on the nodes. Several potential problems are used to establish the validity of the coupled method.