OOIR: Observatory of International Research

Papers

(The TQCC of SIAM Journal on Numerical Analysis is 5. 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 2020-05-01 to 2024-05-01.)

Article	Citations
Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Convergence Analysis	35
High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation	28
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows	27
A General Framework of Low Regularity Integrators	25
Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field	25
A Structure-Preserving Parametric Finite Element Method for Surface Diffusion	24
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case	23
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis	22
An Artificial Compressibility Crank--Nicolson Leap-Frog Method for the Stokes--Darcy Model and Application in Ensemble Simulations	21
Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights	21
Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations	20
Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers	19
Computational Methods for First-Order Nonlocal Mean Field Games with Applications	19
Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences	19
Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data	18
Time Integration of Tree Tensor Networks	17
Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance	16
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion	16
Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows	15
Local Energy Estimates for the Fractional Laplacian	15
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions	15
Discovery of Dynamics Using Linear Multistep Methods	15
An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws	14
Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit	14
Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization	14

Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity	14
Approximation of High-Dimensional Periodic Functions with Fourier-Based Methods	14
A Family of Finite Element Stokes Complexes in Three Dimensions	13
Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations	13
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties	13
A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation	13
Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems	13
Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier--Stokes Equations with Periodic Boundary Conditions	13
A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients	13
Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization	12
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition	12
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving	12
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem	12
A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$	11
Strong Convergence of Full Discretization for Stochastic Cahn--Hilliard Equation Driven by Additive Noise	11
Temporal Second-Order Finite Difference Schemes for Variable-Order Time-Fractional Wave Equations	11
Error Estimates for the Optimal Control of a Parabolic Fractional PDE	11
Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models	11
Divergence-free Scott--Vogelius Elements on Curved Domains	11
Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities	10
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion	10
Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates	10
The Energy Technique for the Six-Step BDF Method	10
Modeling and Analysis of the Coupling in Discrete Fracture Matrix Models	10
Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements	10
Rank-Adaptive Time Integration of Tree Tensor Networks	9
${H^m}$-Conforming Virtual Elements in Arbitrary Dimension	9
A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics	9
On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization	9
Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential	9
Finite Elements for div- and divdiv-Conforming Symmetric Tensors in Arbitrary Dimension	9
Carleman-Based Reconstruction Algorithm for Waves	9
The Connections Between Lyapunov Functions for Some Optimization Algorithms and Differential Equations	9
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems	9
Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System	8
Asymptotically-Preserving Large Deviations Principles by Stochastic Symplectic Methods for a Linear Stochastic Oscillator	8
Optimal Error Analysis of Euler and Crank--Nicolson Projection Finite Difference Schemes for Landau--Lifshitz Equation	8
Computing Semigroups with Error Control	8
Positivity of Discrete Time-Fractional Operators with Applications to Phase-Field Equations	8
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems	8
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part II: Optimal Convergence	8
Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations	8
Locking-Free Enriched Galerkin Method for Linear Elasticity	8
An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation	8
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property	8
Uniformly Accurate Low Regularity Integrators for the Klein--Gordon Equation from the Classical to NonRelativistic Limit Regime	7
A Variable Time Step Time Filter Algorithm for the Geothermal System	7
Error Estimates for Euler Discretization of High-Index Saddle Dynamics	7
Analysis of Error Localization of Chebyshev Spectral Approximations	7
Approximating Linear Response by Nonintrusive Shadowing Algorithms	7

Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains	7
Local Convergence of the FEM for the Integral Fractional Laplacian	7
Hybrid Localized Spectral Decomposition for Multiscale Problems	7
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part I: Uniform Stability	7
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation	7
Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version	6
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes	6
On the Sobolev and $L^p$-Stability of the $L^2$-Projection	6
An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions	6
Approximation of Smoothness Classes by Deep Rectifier Networks	6
A Narrow-stencil Finite Difference Method for Approximating Viscosity Solutions of Hamilton--Jacobi--Bellman Equations	6
A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation	6
MINRES for Second-Order PDEs with Singular Data	6
Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps	6
Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation	6
Low-Rank Updates of Matrix Functions II: Rational Krylov Methods	6
Stability of Variable-Step BDF2 and BDF3 Methods	6
Summation-by-Parts Operators for General Function Spaces	6
A Semi-implicit Exponential Low-Regularity Integrator for the Navier--Stokes Equations	6
Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems	6
A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed Curves	6
A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm	5
Strong Convergence of a Verlet Integrator for the Semilinear Stochastic Wave Equation	5
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion	5
A Convergent Structure-Preserving Finite-Volume Scheme for the Shigesada--Kawasaki--Teramoto Population System	5
Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides	5
A Polynomial-Degree-Robust A Posteriori Error Estimator for Nédélec Discretizations of Magnetostatic Problems	5
Improving Accuracy of the Fifth-Order WENO Scheme by Using the Exponential Approximation Space	5
A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation	5
A Fourth-Order Unfitted Characteristic Finite Element Method for Solving the Advection-Diffusion Equation on Time-Varying Domains	5
Convergence in Total Variation of the Euler--Maruyama Scheme Applied to Diffusion Processes with Measurable Drift Coefficient and Additive Noise	5
A Symplectic Discontinuous Galerkin Full Discretization for Stochastic Maxwell Equations	5
Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow	5
Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems	5
${\boldsymbol{H^1}}$ -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation	5
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization	5
Convergence Analysis of Discrete High-Index Saddle Dynamics	5
Reciprocal-Log Approximation and Planar PDE Solvers	5
Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere	5
Analysis of Lowest-Order Characteristics-Mixed FEMs for Incompressible Miscible Flow in Porous Media	5
Neural Parametric Fokker--Planck Equation	5
Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem	5