A fully automatic hp-adaptivity for elliptic PDEs in three dimensions

We present an algorithm that determines an optimal refinement strategy for a given finite element mesh. The algorithm automatically selects optimal (possibly anisotropic) h-refinements and distribution of (also anisotropic) order of approximation p. The local selection between h-refinement and p-enrichment is made to decrease the projection-based interpolation error of a reference (fine grid) solution with maximum rate with respect to the number of local degrees of freedom (dof) added. A reconciliation step maintains the 1-irregularity of the mesh. When applied iteratively, the algorithm delivers exponential convergence in the energy norm for model elliptic problems with singular or nearly singular solutions.