The quasi-uniformity condition for reproducing kernel element method meshes

The reproducing kernel element method is a hybrid between finite elements and meshfree methods that provides shape functions of arbitrary order and continuity yet retains the Kronecker-δ property. To achieve these properties, the underlying mesh must meet certain regularity constraints. This paper develops a precise definition of these constraints, and a general algorithm for assessing a mesh is developed. The algorithm is demonstrated on several mesh types. Finally, a guide to generation of quasi-uniform meshes is discussed.