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

Authors:
Anna Paszyńska;Maciej Paszyński;Ewa Grabska
Affiliations:
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Cracow, Poland 30-059;Department of Computer Science, AGH University of Science and Technology, Cracow, Poland 30-059;Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Cracow, Poland 30-059
Venue:
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Year:
2009

Citing 2
Cited 1

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

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Fundamenta Informaticae

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Abstract

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.