Effective and practical h–p‐version adaptive analysis procedures for the finite element method

Two practical and effective, h–p-type, finite element adaptive procedures are presented. The procedures allow not only the final global energy norm error to be well estimated using hierarchic p-refinement, but in addition give a nearly optimal mesh. The design of this is guided by the local information computed on the previous mesh. The desired accuracy can always be obtained within one or at most two h–p-refinements. The rate of convergence of the adaptive h–p-version analysis procedures has been tested for some examples and found to be very strong. The presented procedures can easily be incorporated into existing p- or h-type code structures.