Lng Fem: Generating Graded Meshes and Solving Elliptic Equations on 2-d Domains of Polygonal Structures

We develop LNG FEM, a software package for graded mesh generation and for solving elliptic equations. LNG FEM generates user-specified graded meshes on arbitrary two-dimensional domains with straight edges, for different boundary conditions, once initial information is passed to the program by appropriately filling out some source files. We focus on a detailed instruction on the implementation of the software after a brief literature review of elliptic boundary value problems and graded meshes. Then, we show examples to point out that LNG FEM is equipped with advanced algorithms and data structures to perform efficiently. LNG FEM is to popularize the use and understanding of graded mesh in the finite element method. We hope it triggers more interest and discoveries both in academia and in industry.