Solving a suite of NIST benchmark problems for adaptive FEM with the Hermes library

Recently, a new suite of twelve benchmark problems for adaptive finite element methods (FEM) was published at the US National Institute for Standards and Technology (NIST). These benchmark problems come with exact solutions, and they exhibit all typical difficulties associated with elliptic problems including singularities, steep internal layers, anisotropy, and oscillations. In this paper we solve these benchmark problems using the open source library Hermes (http://hpfem.org). All these results are reproducible—they are part of the Git repository of the open source Hermes project, and the reader can experiment with them by himself/herself. Instructions for this are provided. We hope that authors of other adaptive FEM codes will make their results for these test problems available in a reproducible fashion as well.