Hermes

Hermes hp-FEM & hp-DG Library

Hermes is a C++ library for rapid development of adaptive hp-FEM / hp-DG solvers. Novel hp-adaptivity algorithms help solve a large variety of problems ranging from ODE and stationary linear PDE to complex time-dependent nonlinear multiphysics PDE systems.


Hermes version 3.0 is coming soon together with a new version of <a href=”http://www.agros2d.org”>Agros2D</a>. The new version of Hermes brings several new features, such as DG limiters, Taylor L2 shapeset, MATIO import / export of algebraic structures, as well as lots of optimizations, both CPU-related, and memory-related.

Highlights of Hermes Capabilities

Mathematical Point of View

  • L2, H1, HCurl, HDiv Sobolev spaces, polynomial degree up to 10
  • Hanging nodes of arbitrary order
  • Multimesh: component-specific meshes w/o projections or interpolations
  • Time-adaptivity with multitude of pre-implemented Runge-Kutta methods
  • Coupled problems solved together with hp-DG and hp-FEM
  • hp-Adaptivity based on reference solution and local projections
space_time_adaptivity
Space-time adaptivity
dynamical_meshes
Dynamical meshes
curved_elementsadaptive_multimesh_hp-FEM
Curved elements
See more in the Gallery.

Implementation Point of view