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Using a graph grammar system in the finite element method. (English) Zbl 1284.68335

Summary: 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.

MSC:

68Q42 Grammars and rewriting systems
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
68R10 Graph theory (including graph drawing) in computer science
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