OOIR: Observatory of International Research

Papers

(The TQCC of SIAM Journal on Numerical Analysis is 6. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-11-01 to 2024-11-01.)

Article	Citations
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows	38
Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Convergence Analysis	37
High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation	34
Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field	31
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case	28
A General Framework of Low Regularity Integrators	27
A Structure-Preserving Parametric Finite Element Method for Surface Diffusion	27
An Artificial Compressibility Crank--Nicolson Leap-Frog Method for the Stokes--Darcy Model and Application in Ensemble Simulations	26
Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers	25
Computational Methods for First-Order Nonlocal Mean Field Games with Applications	23
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis	23
Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences	22
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving	21
Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data	21
Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity	21
Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations	21
Time Integration of Tree Tensor Networks	21
Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights	21
Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations	20
An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws	19
Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance	19
Discovery of Dynamics Using Linear Multistep Methods	19
Approximation of High-Dimensional Periodic Functions with Fourier-Based Methods	18
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions	18
Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit	17

Local Energy Estimates for the Fractional Laplacian	17
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion	17
A Family of Finite Element Stokes Complexes in Three Dimensions	17
Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows	17
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties	17
Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier--Stokes Equations with Periodic Boundary Conditions	17
Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization	16
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem	16
Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models	16
A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients	16
Finite Elements for div- and divdiv-Conforming Symmetric Tensors in Arbitrary Dimension	15
A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation	15
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems	15
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition	14
The Energy Technique for the Six-Step BDF Method	14
Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization	14
Error Estimates for the Optimal Control of a Parabolic Fractional PDE	14
Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems	13
Temporal Second-Order Finite Difference Schemes for Variable-Order Time-Fractional Wave Equations	13
Locking-Free Enriched Galerkin Method for Linear Elasticity	13
Stability of Variable-Step BDF2 and BDF3 Methods	12
Divergence-free Scott--Vogelius Elements on Curved Domains	12
A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$	12
Local Convergence of the FEM for the Integral Fractional Laplacian	12
A Variable Time Step Time Filter Algorithm for the Geothermal System	12
Carleman-Based Reconstruction Algorithm for Waves	11
Optimal Error Analysis of Euler and Crank--Nicolson Projection Finite Difference Schemes for Landau--Lifshitz Equation	11
Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities	11
Strong Convergence of Full Discretization for Stochastic Cahn--Hilliard Equation Driven by Additive Noise	11
Computing Semigroups with Error Control	10
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part II: Optimal Convergence	10
Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations	10
Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System	10
Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates	10
On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization	10
Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential	10
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion	10
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems	10
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part I: Uniform Stability	10
Rank-Adaptive Time Integration of Tree Tensor Networks	10
Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements	10
${H^m}$-Conforming Virtual Elements in Arbitrary Dimension	10
Modeling and Analysis of the Coupling in Discrete Fracture Matrix Models	10
A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics	10
The Connections Between Lyapunov Functions for Some Optimization Algorithms and Differential Equations	10
Positivity of Discrete Time-Fractional Operators with Applications to Phase-Field Equations	9
Error Estimates for Euler Discretization of High-Index Saddle Dynamics	9
A Semi-implicit Exponential Low-Regularity Integrator for the Navier--Stokes Equations	9
Asymptotically-Preserving Large Deviations Principles by Stochastic Symplectic Methods for a Linear Stochastic Oscillator	9
${\boldsymbol{H^1}}$ -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation	9

Hybrid Localized Spectral Decomposition for Multiscale Problems	9
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations	9
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property	9
Analysis of Error Localization of Chebyshev Spectral Approximations	8
MINRES for Second-Order PDEs with Singular Data	8
An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions	8
An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation	8
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation	8
Uniformly Accurate Low Regularity Integrators for the Klein--Gordon Equation from the Classical to NonRelativistic Limit Regime	8
A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed Curves	8
On the Sobolev and $L^p$-Stability of the $L^2$-Projection	8
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes	8
Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere	8
Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version	8
A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm	8
Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains	7
Stability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP Property	7
A Narrow-stencil Finite Difference Method for Approximating Viscosity Solutions of Hamilton--Jacobi--Bellman Equations	7
Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides	7
Low-Rank Updates of Matrix Functions II: Rational Krylov Methods	7
Neural Parametric Fokker--Planck Equation	7
Optimal $\boldsymbol{{L^2}}$ Error Estimates of Unconditionally Stable Finite Element Schemes for the Cahn–Hilliard–Navier–Stokes System	7
A Fourth-Order Unfitted Characteristic Finite Element Method for Solving the Advection-Diffusion Equation on Time-Varying Domains	7
Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation	7
A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation	7
Improving Accuracy of the Fifth-Order WENO Scheme by Using the Exponential Approximation Space	7
Approximating Linear Response by Nonintrusive Shadowing Algorithms	7
A Polynomial-Degree-Robust A Posteriori Error Estimator for Nédélec Discretizations of Magnetostatic Problems	7
Strong Convergence of a Verlet Integrator for the Semilinear Stochastic Wave Equation	6
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion	6
Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow	6
Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps	6
Efficient Approximation of SDEs Driven by Countably Dimensional Wiener Process and Poisson Random Measure	6
Error Estimate of Unconditionally Stable and Decoupled Linear Positivity-Preserving FEM for the Chemotaxis-Stokes Equations	6
Convergence in Total Variation of the Euler--Maruyama Scheme Applied to Diffusion Processes with Measurable Drift Coefficient and Additive Noise	6
Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems	6
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization	6
A Local Discontinuous Galerkin Approximation for thep-Navier–Stokes System, Part I: Convergence Analysis	6
Frequency-Explicit A Posteriori Error Estimates for Finite Element Discretizations of Maxwell's Equations	6
Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations	6
Reciprocal-Log Approximation and Planar PDE Solvers	6
Summation-by-Parts Operators for General Function Spaces	6
Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems	6
Approximation of Smoothness Classes by Deep Rectifier Networks	6