<div class="csl-bib-body">
<div class="csl-entry">Karkulik, M., Melenk, J. M., & Rieder, A. (2025). On interpolation spaces of piecewise polynomials on mixed meshes. <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, <i>59</i>(1), 231–264. https://doi.org/10.1051/m2an/2024069</div>
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dc.identifier.issn
2822-7840
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/212069
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dc.description.abstract
We consider fractional Sobolev spaces Hθ, θ ϵ (0, 1), on 2D domains and H¹-conforming discretizations by globally continuous piecewise polynomials on a mesh consisting of shape-regular triangles and quadrilaterals. We prove that the norm obtained from interpolating between the discrete space equipped with the L²-norm on the one hand and the H¹-norm on the other hand is equivalent to the corresponding continuous interpolation Sobolev norm, and the norm-equivalence constants are independent of meshsize and polynomial degree. This characterization of the Sobolev norm is then used to show an inverse inequality between H¹ and Hθ
en
dc.language.iso
en
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dc.publisher
EDP Sciences
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dc.relation.ispartof
ESAIM: Mathematical Modelling and Numerical Analysis
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dc.subject
Domain decomposition
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dc.subject
Interpolation spaces
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dc.subject
Inverse estimates
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dc.subject
Stable localization
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dc.title
On interpolation spaces of piecewise polynomials on mixed meshes
