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Bounded commuting projections for multipatch spaces with non-matching interfaces
Martin Campos Pinto1; Frederik Schnack1
1 Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, 85748 Garching, Germany
The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 85-137.

We present commuting projection operators on de Rham sequences of two-dimensional multipatch spaces with local tensor-product parametrization and non-matching interfaces. Our construction yields projection operators which are local and stable in any $L^p$ norm with $p \in [1,\infty ]$: it applies to shape-regular spline patches with different mappings and resolutions, under the assumption that interior vertices are shared by exactly four patches, and that neighboring patches have nested resolutions in a way that excludes local chessboard patterns. Our construction also applies to de Rham sequences with homogeneous boundary conditions. Following a broken-FEEC approach, we first consider tensor-product commuting projections on the single-patch de Rham sequences, and modify the resulting patch-wise operators so as to enforce their conformity and commutation with the global derivatives, while preserving their projection and stability properties with constants independent of both the diameter and inner resolution of the patches.

Published online:
DOI: 10.5802/smai-jcm.120
Classification: 65N30, 65N12, 65D07
Keywords: Commuting projection, finite element exterior calculus, de Rham sequence, multipatch spaces, isogeometric analysis

Martin Campos Pinto 1; Frederik Schnack 1

1 Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, 85748 Garching, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Martin Campos Pinto; Frederik Schnack. Bounded commuting projections for multipatch spaces with non-matching interfaces. The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 85-137. doi : 10.5802/smai-jcm.120. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.120/

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