Quadrilateral approaches for accurate free mesh method

This paper presents the formulation of free mesh method and two approaches of the method by incorporating quadrilateral elements. The approaches do not have any di!erence with the original free mesh method in their fundamental algorithms, wherein local system equations with triangular elements are created nodewise to create the global system equations, and their implementation is therefore very easy. The "rst approach creates quadrilateral elements inside every triangular element, whilst quadrilateral elements are generated outside every triangular element in the second approach. The results of numerical examples indicate that the approaches improve the accuracy of free mesh method, further opening the possibility for more improvement using an accurate quadrilateral element