Mesh based construction of flat-top partition of unity functions

A novel idea to construct flat-top partition of unity functions in a closed form on a general (structured or unstructured) finite element mesh is presented. An efficient and practical construction method of a flat-top partition of unity function is important in the generalized finite element method (GFEM). Details on how to construct flat-top partition of unity functions on a provided mesh are given. The generalized finite element approximation with the use of the new flat-top partition of unity function is presented with various numerical examples that demonstrate the effectiveness of proposed flat-top partition of unity functions.