Applying the hp–d version of the FEM to locally enhance dimensionally reduced models

A modification of the hp–d method is presented, which allows to locally enhance a dimensionally reduced finite element approximation with an Ansatz based on a more accurate, i.e. dimensionally higher, model. The procedure is based on a hierarchical domain decomposition which is applied to couple discretizations of different types of mechanical models, like beams, plates and solids. Thereby, the error of the underlying mathematical model can be reduced in critical regions by introducing locally a physically more sophisticated model. Two examples are given to demonstrate the basic properties of the proposed method. In the first example the solution of a one-dimensional beam model is improved locally by a two-dimensional finite element computation. In the second example the local enhancement of a Reissner–Mindlin plate by a fully three-dimensional continuum approach is considered, yielding a significant reduction of the model error.