Graph Transformations for Modeling hp-Adaptive Finite Element Method with Mixed Triangular and Rectangular Elements

The paper presents composition graph (CP-graph) grammar, which consists of a set of CP-graph transformations, suitable for modeling transformations of two dimensional meshes with rectangular elements mixed with triangular elements. The mixed meshes are utilized by the self-adaptive hp Finite Element Method (FEM) extended to support triangular and rectangular elements. The hp -FEM generates a sequence of mixed triangular and rectangular element meshes providing exponential convergence of the numerical error with respect to the mesh size. This is done be executing several h or p refinements over an initial mesh. The mixed finite element mesh is represented by attributed CP-graph. The proposed graph transformations model the initial mesh generation as well as mesh refinements. The proposed extended graph grammar has been defined and verified by using implemented software.