Introduces a conforming liftings framework that bridges virtual-function and fully discrete convergence analysis techniques for polytopal methods and demonstrates it on a model problem while linking to discrete differential complexes.
Finite Elements II
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A Rocq formalization defines simplicial Lagrange finite elements as records with geometric data, polynomial approximations, and unisolvence proofs for any dimension and polynomial degree.
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
A finite element method with divergence reconstruction for generalized Navier-Stokes equations valid for p > 2d/(d+2), with a priori error estimates for velocity and pressure.
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Key challenges and bridges among convergence analysis techniques for polytopal methods
Introduces a conforming liftings framework that bridges virtual-function and fully discrete convergence analysis techniques for polytopal methods and demonstrates it on a model problem while linking to discrete differential complexes.
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A Rocq Formalization of Simplicial Lagrange Finite Elements
A Rocq formalization defines simplicial Lagrange finite elements as records with geometric data, polynomial approximations, and unisolvence proofs for any dimension and polynomial degree.
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Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
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Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents
A finite element method with divergence reconstruction for generalized Navier-Stokes equations valid for p > 2d/(d+2), with a priori error estimates for velocity and pressure.