We construct a local Fortin projection for the Scott–Vogelius finite element pair for polynomial degree k ≥ 4 on general shape-regular triangulations in two dimensions. In particular, the triangulation may contain singular vertices. In addition to preserving the divergence in the dual of the pressure space, the projection preserves discrete boundary data and satisfies local stability estimates.
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Eickmann et al. (2026) studied this question.
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