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arXiv · 2609.11496

Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions

Thomas Führer·Gregor Gantner·Roberto González·Michael Karkulik
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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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Thomas Führer, Gregor Gantner, Roberto González, Michael Karkulik. 2026-09-10. Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions. https://arxiv.org/abs/2609.11496

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