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arXiv · 2609.04926

Construction of trace-preserving Fortin operators

Franziska Eickmann·Tabea Tscherpel
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Abstract

We present a unifying framework to construct local Fortin operators for conforming mixed finite element pairs for the Stokes equations. The operators are constructed to satisfy the divergence-preservation property, local stability and approximation properties, and certain trace-preservation properties. For the latter, some of the finite element pairs require an enrichment of the velocity space. We present the construction for the $P_d-P_0$ element, the Bernardi-Raugel element, the conforming Crouzeix-Raviart element, a modified MINI element and generalised Taylor-Hood elements. Furthermore, we discuss implications of the existence of such a Fortin operator beyond inf-sup stability. These include applications to non-Newtonian fluid flow, problems with inhomogeneous Dirichlet boundary conditions, as well as uniform inf-sup stability relevant for domain approximation and moving domains.

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Franziska Eickmann, Tabea Tscherpel. 2026-09-04. Construction of trace-preserving Fortin operators. https://arxiv.org/abs/2609.04926

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