Hypergraph Grammars in hp-adaptive Finite Element Method

AbstractThe paper presents the hypergraph grammar for modelling the hp-adaptive finite element method algorithm with rectangular elements. The finite element mesh is represented by a hypergraph. All mesh transformations are modelled by means of hypergraph grammar rules. These rules allow to generate the initial mesh, to assign values of polynomial order to the element nodes, to generate the matrix for each element, to solve the problem and to perform the hp-adaptation