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1 2013

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Using a graph grammar system in the finite element method

Strug B., Paszyńska A., Paszyński M., Grabska E.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 4

839--853

The paper presents a system of Composite Graph Grammars (CGGs)modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element nodes and perform h- and p-adaptations. The CGG system is illustrated with an example from the domain of geophysics.