ngstSpaceKit is an add-on to ngsolve and ngstrefftz, and provides a collection of finite element spaces. The goal of this project is to explore possibilities of the conforming Trefftz Method, and provide concrete example uses for it.

Implemented Spaces

ngstSpaceKit implements a series of well-known finite elements, that are not yet implemented in ngsolve:

• Argyris
• Bogner-Fox-Schmitt
• Crouzeix-Falk
• Hermite
• Morley

On top of that, there are other exotic spaces defined:

• a weakly H1-conforming element, with the option to use the inner dofs with an embedded Trefftz formulation
• an H(div)-conforming element, with the option to use the inner dofs with an embedded Trefftz formulation
• a Stokes mixed element, where the velocity part is weakly H(div)-conforming, and the remaining dofs adhering to a Stokes embedded Trefftz formulation
• a P1 / Q1 Immersed Finite Element Space, which is suitable to solve interface problems on a domain with a cut. Refer to Lin et al. for a proper introduction of the Immersed Finite Element method.

For demonstration purposes, there are some spaces implemented, which already have a native ngsolve implementation:

• Brezzi-Douglas-Marini
• Crouzeix-Raviart

Citing

ngstSpaceKit is published on Zenodo. You may cite it as

Meyer, J. C., & Lehrenfeld, C. (2025). ngstSpaceKit. Zenodo. https://doi.org/10.5281/zenodo.17281221

License

ngstSpaceKit is available under the LGPL-3.0 license.