So far we have not paid any attention to the accuracy of results. In general, computations on a fixed mesh are not very accurate and they should not be trusted. Controlled accuracy can be achieved through adaptive mesh refinement (AMR). Advanced adaptive higher-order FEM (hp-FEM) is one of the main strengths of Hermes. With eight modes of automatic hp-adaptivity, Hermes excels at delivering highly accurate results with much lower numbers of degrees of freedom than conventional FEM codes.