The BDF2 tangent-plane FEM for LLG achieves optimal a-priori rates O(h+τ²) under regularity, completing the first higher-order linear scheme convergent to both weak and strong solutions.
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16 Pith papers cite this work, alongside 3,849 external citations. Polarity classification is still indexing.
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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.
The continuous LBB constant for Stokes flow among periodic pillars decays as m^{-1}, inducing O(m^2) Schur conditioning; an adaptively scaled AL method with γ ∝ m² restores robust iteration counts.
A pure-pseudostress mixed FEM for the elasticity eigenproblem is locking-free, needs no symmetry constraint, and comes with a priori and residual a-posteriori error estimates that remain valid as Poisson ratio approaches 1/2.
An explicit budget allocation condition is derived for two-stage kernel-based operator learning, relating training set size, input observations, and output resolution, alongside a physics-informed online reconstruction extension.
Proves that the p-th order EERK method for semilinear parabolic problems with initial regularity γ achieves convergence rate min(1 + γ/2 + ρ1(γ)/2, p).
A dimension-dependent approximate Carathéodory theorem yields explicit contraction rates for Delaunay mesh refinement that exceed those of standard subdivision.
Derives reliable and efficient a posteriori error estimators for a general class of stabilized finite element methods applied to time-dependent mean field games, with an improved version for specific mass-lumping and affine-preserving stabilizations.
Develops and analyzes a second-order explicit partitioned scheme for the time-dependent Stokes-Biot problem with stability under parabolic CFL and error bounds of order h^k + k^2.
Mixed VEM with novel non-linear stabilization for p-Laplace equation, establishing non-Hilbertian inf-sup stability, continuity, coercivity, and a priori error estimates.
Develops an evolving finite element method for parabolic PDEs with evolving interfaces, derives a suitable weak formulation, proves optimal error bounds for isoparametric elements of arbitrary order, and verifies convergence numerically.
A combined linear and nonlinear stabilization for continuous Galerkin finite elements on the transport equation yields localized a priori error bounds of order O(h^{k+1/2}) in the final-time L2 norm under local regularity assumptions.
An adaptive hyperviscosity stabilization for RBF-FD is proposed that sets the constant from the spectral radius of the evolution matrix, supports general nodes, and is demonstrated on linear advection and Burgers' equation with limited dissipation.
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
SAETASS solves the time-dependent astroparticle transport equation in spherical symmetry using a conservative finite-volume, operator-splitting framework, validated against analytical solutions and applied to cosmic-ray proton transport in a stellar-wind bubble.
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BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates
The BDF2 tangent-plane FEM for LLG achieves optimal a-priori rates O(h+τ²) under regularity, completing the first higher-order linear scheme convergent to both weak and strong solutions.
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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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Sharp inf-sup estimate for the Stokes equation in tight domains with periodic pillars and some numerical implications
The continuous LBB constant for Stokes flow among periodic pillars decays as m^{-1}, inducing O(m^2) Schur conditioning; an adaptively scaled AL method with γ ∝ m² restores robust iteration counts.
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A locking free mixed FEM based on a pure pseudostress based formulation for the elasticity eigenproblem
A pure-pseudostress mixed FEM for the elasticity eigenproblem is locking-free, needs no symmetry constraint, and comes with a priori and residual a-posteriori error estimates that remain valid as Poisson ratio approaches 1/2.
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Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
An explicit budget allocation condition is derived for two-stage kernel-based operator learning, relating training set size, input observations, and output resolution, alongside a physics-informed online reconstruction extension.
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Higher-order exponential Runge-Kutta Galerkin finite element method for semilinear parabolic problems with nonsmooth data
Proves that the p-th order EERK method for semilinear parabolic problems with initial regularity γ achieves convergence rate min(1 + γ/2 + ρ1(γ)/2, p).
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Sharp approximate Carath\'eodory theorem and application to iterated Delaunay refinement
A dimension-dependent approximate Carathéodory theorem yields explicit contraction rates for Delaunay mesh refinement that exceed those of standard subdivision.
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A posteriori error bounds for finite element approximations of time-dependent mean field games
Derives reliable and efficient a posteriori error estimators for a general class of stabilized finite element methods applied to time-dependent mean field games, with an improved version for specific mass-lumping and affine-preserving stabilizations.
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Second order explicit splitting scheme for fluid-poroelastic structure interaction problems
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Mixed VEM with novel non-linear stabilization for p-Laplace equation, establishing non-Hilbertian inf-sup stability, continuity, coercivity, and a priori error estimates.
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Local error estimates for a finite element method combining linear and nonlinear stabilization for the linear hyperbolic transport equation
A combined linear and nonlinear stabilization for continuous Galerkin finite elements on the transport equation yields localized a priori error bounds of order O(h^{k+1/2}) in the final-time L2 norm under local regularity assumptions.
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Adaptive hyperviscosity stabilisation for the RBF-FD method in solving advection-dominated transport equations
An adaptive hyperviscosity stabilization for RBF-FD is proposed that sets the constant from the spectral radius of the evolution matrix, supports general nodes, and is demonstrated on linear advection and Burgers' equation with limited dissipation.
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GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms
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