Automatic hp-adaptivity

One of the main strengths of the Hermes library, which is also available in Agros2D, is an automatic hp-adaptivity algorithm. It combines advantages of the h-adaptivity (precise resolution of singularities, boundary layers, etc.) with advantages of p-adaptivity, which is very successful for smooth solutions. Its superiority can bee seen from the following graph, where different adaptivity strategies are compared for a test problem.

Even though hp-adaptivity is a very successful strategy, it may not be suitable for all situations. Agros2D, therefore, allows the user chosing between h, p or hp-adaptivity or to decide not to use the adaptivity at all. In that case, a-priori knowledge of the solution character may be used to prepare the mesh appropriately using various operations, such as refinements towards vertices, edges, etc. The dimensions of elements and their orders may also be selected by the user.

  • Solin, P., Cerveny, J., Dolezel, I.: Arbitrary-Level Hanging Nodes and Automatic Adaptivity in the hp-FEM, Math. Comput. Simul., 2008, Volume 77, pp 117 – 132, DOI 10.1016/j.matcom.2007.02.011