Coupled 3D-2D model for heat equation

The coupling of different dimensionalities in finite element modelling is presented. The whole coupled model is presented with coupled matrices that combine the matrices of higher and lower dimensional models into one matrix. The matrices of the finite element model are first calculated separately for 3D and 2D models and then these matrices are combined using suitable scaling factors and off-diagonal terms that couple the 3D and 2D parts. The method applies to problems where the lower dimensional model is a relatively good approximation to the higher dimensional model. The results show that the coupled model gives similar results to full 3D or 2D models but with a significantly lower number of elements.