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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 · 0 citations
Preprint Sep 2026

An adaptive localized orthogonal decomposition method for Helmholtz problems

We develop an adaptive localized orthogonal decomposition (ALOD) method for Helmholtz problems with localized oscillations and singularities. The main result is the first wavenumber-robust residual a posteriori error estimate for a Helmholtz LOD discretization within the standard resolution, oversampling, and discrete-...

Yuwen Li, Chu-Xin Que · 0 citations

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