Abstract
In this paper we present an application of graph grammar for modelling a three dimensional hp adaptive finite element method for multi-physics simulations. The graph grammar model involves the process of generation of the mesh with tetrahedral finite elements, the process of mesh adaptation by means of h refinement as well as interfacing with the multi-frontal solver algorithm by translating the finite elements into a sequence of frontal matrices, being an input for the multi-frontal solver algorithm. The paper is concluded with numerical results concerning an advanced multi-physics problems, the propagation of an acoustic waves over the model of the human head.