Development and analysis of structure-preserving finite element methods on non-conforming meshes
Abstract
This work develops structure-preserving finite element methods on two-dimensional refined multipatch spaces. Within the broken-FEEC framework, we construct bounded commuting projections on non-matching discretizations with certain assumptions on the geometry. We also design conforming projections, based on interface-averaging and extension-restriction operators, enabling spurious-free numerical schemes. Additionally, strong-strong discretizations are extended to multipatch setups.
BibTeX
@phdthesis{dissertation,
author = {Schnack, Frederik Günter},
title = {Development and analysis of structure-preserving finite element methods on non-conforming meshes},
year = {2025},
school = {Technische Universität München},
pages = {161},
language = {en},
abstract = {This work develops structure-preserving finite element methods on two-dimensional refined multipatch spaces. Within the broken-FEEC framework, we construct bounded commuting projections on non-matching discretizations with certain assumptions on the geometry.
We also design conforming projections, based on interface-averaging and extension-restriction operators, enabling spurious-free numerical schemes. Additionally, strong-strong discretizations are extended to multipatch setups.},
keywords = {},
note = {},
url = {https://mediatum.ub.tum.de/1776749},
doi = {},
}