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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.

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