Multiscale computations with a combination of the h- and p-versions of the finite-element method

The numerical treatment of structural problems is often difficult if the global system behavior is affected by phenomena on different length scales. When simulating multiscale problems, it is essential to find a discretization that equally reflects all aspects of the problem with sufficient accuracy. The present paper is concerned with the formulation of a finite-element procedure which combines the p-method to resolve global features of a problem with an h-method to resolve local features. Thus the advantageous properties of both standard procedures can be optimally exploited. The implementation provides the further advantage that the numerical treatment of the problems on the different length scales can be done with independent finite-element discretizations. To solve the overall problem, an iteration scheme with an adaptive solution strategy is developed. Benchmark problems and an example with relevance to soil mechanics are presented.