Development and analysis of structure-preserving finite element methods on non-conforming meshes

Frederik Schnack

2025-10-28 · PhD · PSYDAC

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 = {},
}