Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11496

Authors: Führer, Thomas, Gantner, Gregor, González, Roberto, Karkulik, Michael

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

OpenAlex ID: W7212253280

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