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

  • Anna Paszyńska
  • Maciej Paszyński
  • Ewa Grabska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5103)


The paper presents composition graph (CP-graph) grammar, which consists of a set of CP-graph transformations, suitable for modeling triangular finite element mesh transformations utilized by the self-adaptive hp Finite Element Method (FEM). The hp adaptive FEM allows to utilize distributed computational meshes, with finite elements of various size (thus h stands for element diameter) and polynomial orders of approximation varying locally, on finite elements edges and interiors (thus p stands for polynomial order of approximation). The computational triangular mesh is represented by attributed CP-graph. The proposed graph transformations model the initial mesh generation, procedure of h refinement (breaking selected finite elements into son elements), and p refinement (adjusting polynomial orders of approximation on selected element edges and interiors). The graph grammar has been defined and verified by implemented graph grammar transformation software tool.


Finite Element Method Polynomial Order Graph Transformation Initial Mesh Adjacent Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Anna Paszyńska
    • 1
  • Maciej Paszyński
    • 2
  • Ewa Grabska
    • 1
  1. 1.Faculty of Physics, Astronomy and Applied Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.Department of Computer ScienceAGH University of Science and TechnologyKrakówPoland

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