Our group and its goals

Our group is the leader in the development of adaptive higher-order finite element methods (hp-FEM) for engineering and scientific problems described by partial differential equations (PDE). We develop exclusively PDE-independent methods, so that practitioners do not have to think twice whether they can use them or not.

The hp-FEM was invented in the 1980s and its extremely fast, exponential convergence was first demonstrated on simple 1D elliptic problems (see the Wikipedia page). The exponential convergence makes the hp-FEM vastly superior to standard engineering FEM. However, the hp-FEM algorithms have not yet matured enough to be adopted broadly by practitioners. It is our goal to change this and to make adaptive hp-FEM the standard tool for the solution of PDE models in many areas of engineering and science.

To disseminate adaptive hp-FEM to practitioners, we have developed novel algorithms and software that are freely available through the open source projects Hermes, Agros and FEMhub. You can even try them on-line via an interactive web notebook, without having to install any software.

Open Source Projects Hermes, Agros, and FEMhub

• Hermes is a modular C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. All algorithms are PDE-independent, which means that you can use Hermes to emply adaptive hp-FEM to any PDE problem. In more complicated multiphysics problems, different physical fields can be approximated on individual meshes that evolve dynamically in time independently of each other. For more details on this project, visit the Hermes page. Also check out the interactive web notebook.
• Agros is a multiplatform GUI to Hermes developed by the group of Pavel Karban at the University of West Bohemia in Pilsen. In Agros one can define the model interactively or import it from CAD, solve it using adaptive higher-order FEM, and visualize and postprocess the results in many different ways. And the best thing -- all this is for free! For more details, visit the Agros page.
• FEMhub is an open-source distribution featuring finite element codes, along with a web notebook and a unified Python interface. The aim of the project is to allow the user to define his/her problem only once and be able to solve it using various FEM codes easily. This will allow the user to compare advantages and disadvantages of various FEM codes, as well as collaborate in a common open source environment. For more details on this project, visit the FEMhub page.

Interested in Contributing?

We are looking for help! You do not have to be expert in math or FEM since we deal with a variety of problems including web-based computing, interface design, wrappers, etc. The easiest way to see what is going on is to subscribe to our mailing lists:

• FEMhub list, Agros2D list, Hermes2D list, Hermes3D list. General FEM list, group activity list

Both the Hermes and FEMhub home pages contain a list of simpler projects and easy-to-fix issues that we need to do. Naturally, any other useful ideas are welcome as well!

Our Conferences

In order to increase in various engineering and scientific communities the awareness about modern adaptive higher-order computational methods, we organize two series of international conferences: European Seminar on Coupled Problems (ESCO) in Europe and Finite Element Methods in Engineering and Science (FEMTEC) in the U.S. - see the Events page for more details.

The Dark Side of FEM

Do not format your harddisk yet! If the science is not working, maybe it's art. In moments of deepest despair and frustration, visit our gallery Dark Side of FEM!

Acknowledgement

Several students contributed to the project via their M.S. and Ph.D. theses.