PreprintarXiv licencearXiv
A Unified Space-Time Variational Framework for Wave Equations on Differential Forms
Abstract
We revisit a standard space--time variational formulation of the scalar wave equation in the setting of differential forms. For this, we use as spatial operator the nonnegative, self-adjoint (relative) \emph{Hodge--Laplacian} on a bounded Lipschitz domain. Its spectral decomposition reduces the wave problem in any form degree to the same family of scalar ordinary differential equations that underlies existing space-time analysis. We illustrate how this can be used to transfer results from the scalar wave equation with Dirichlet boundary conditions to other wave-type problems. In particular, we connect the framework to perfectly electrically conducting Maxwell problems.
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BibTeX
@misc{urzuatorres2026unified,
title = {{A Unified Space-Time Variational Framework for Wave Equations on Differential Forms}},
author = {C. Urzúa-Torres and A. Wisse},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02136},
eprint = {2611.02136},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02136},
}
RIS
TY - UNPB
TI - A Unified Space-Time Variational Framework for Wave Equations on Differential Forms
AU - C. Urzúa-Torres
AU - A. Wisse
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02136
UR - https://arxiv.org/abs/2611.02136
AB - We revisit a standard space--time variational formulation of the scalar wave equation in the setting of differential forms. For this, we use as spatial operator the nonnegative, self-adjoint (relative) \emph{Hodge--Laplacian} on a bounded Lipschitz domain. Its spectral decomposition reduces the wave problem in any form degree to the same family of scalar ordinary differential equations that underlies existing space-time analysis. We illustrate how this can be used to transfer results from the scalar wave equation with Dirichlet boundary conditions to other wave-type problems. In particular, we connect the framework to perfectly electrically conducting Maxwell problems.
ER -