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Author

Yihanqi Hu

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Preprint Oct 2026

Sparse-grid discretizations of BGG sequences

We develop the first tensor-product sparse-grid finite element discretizations of Bernstein--Gelfand--Gelfand (BGG) complexes. Alpert wavelets and their first and second primitives yield compatible hierarchies of discontinuous, continuous, and continuously differentiable piecewise polynomials, that serve as one-dimensi...

Yihanqi Hu, Yuwen Li · 0 citations
Preprint Aug 2026

Higher-order finite element de Rham complexes on sparse grids

We construct, for the first time, a family of higher-order finite element differential forms on tensor-product sparse grids. The construction starts from compatible one-dimensional spaces of continuous piecewise polynomials and discontinuous piecewise polynomials of one degree lower, linked by differentiation in each c...

Yihanqi Hu, Yuwen Li · 1 citation · ⚡1

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