PreprintarXiv licencearXiv
Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions
Abstract
We construct Scott-Zhang-type space-time quasi-interpolation operators on tensor- product meshes for parabolic settings. Specifically, these are linear and uniformly bounded projections from the classical parabolic energy space onto a space-time tensor-product finite element space that preserve discrete Dirichlet boundary conditions on the lateral space-time boundary. We apply our operator in the context of space-time first-order system least-squares finite elements for parabolic equations to establish a quasi-optimal method for inhomogeneous Dirichlet boundary conditions.
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BibTeX
@misc{fuhrer2026spacetime,
title = {{Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions}},
author = {Thomas Führer and Gregor Gantner and Roberto González and Michael Karkulik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11496},
eprint = {2609.11496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11496},
}
RIS
TY - UNPB
TI - Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions
AU - Thomas Führer
AU - Gregor Gantner
AU - Roberto González
AU - Michael Karkulik
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11496
UR - https://arxiv.org/abs/2609.11496
AB - We construct Scott-Zhang-type space-time quasi-interpolation operators on tensor- product meshes for parabolic settings. Specifically, these are linear and uniformly bounded projections from the classical parabolic energy space onto a space-time tensor-product finite element space that preserve discrete Dirichlet boundary conditions on the lateral space-time boundary. We apply our operator in the context of space-time first-order system least-squares finite elements for parabolic equations to establish a quasi-optimal method for inhomogeneous Dirichlet boundary conditions.
ER -