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 2020-04-01 to 2024-04-01.)

Article	Citations
Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Convergence Analysis	34
High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation	27
Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field	25
A General Framework of Low Regularity Integrators	24
A Structure-Preserving Parametric Finite Element Method for Surface Diffusion	23
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows	22
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis	21
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case	21
An Artificial Compressibility Crank--Nicolson Leap-Frog Method for the Stokes--Darcy Model and Application in Ensemble Simulations	20
Computational Methods for First-Order Nonlocal Mean Field Games with Applications	19
Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights	19
Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences	18
Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations	18
Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers	18
Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data	18
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion	16
Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance	16
Time Integration of Tree Tensor Networks	16
Local Energy Estimates for the Fractional Laplacian	15
Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows	15
Discovery of Dynamics Using Linear Multistep Methods	15
Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit	14
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions	14
Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization	14
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
Approximation of High-Dimensional Periodic Functions with Fourier-Based Methods	13
An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws	13
Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems	13
A Family of Finite Element Stokes Complexes in Three Dimensions	12
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition	12
A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation	12
Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity	12
Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations	12
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties	12
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving	11
Strong Convergence of Full Discretization for Stochastic Cahn--Hilliard Equation Driven by Additive Noise	11
A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$	11
Error Estimates for the Optimal Control of a Parabolic Fractional PDE	11
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem	11
Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization	10
Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements	10
Temporal Second-Order Finite Difference Schemes for Variable-Order Time-Fractional Wave Equations	10
Divergence-free Scott--Vogelius Elements on Curved Domains	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	9
Carleman-Based Reconstruction Algorithm for Waves	9
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion	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
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems	9
Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities	9
The Connections Between Lyapunov Functions for Some Optimization Algorithms and Differential Equations	9
${H^m}$-Conforming Virtual Elements in Arbitrary Dimension	9
Locking-Free Enriched Galerkin Method for Linear Elasticity	8
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property	8
Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations	8
Rank-Adaptive Time Integration of Tree Tensor Networks	8
Computing Semigroups with Error Control	8
Finite Elements for div- and divdiv-Conforming Symmetric Tensors in Arbitrary Dimension	8
Optimal Error Analysis of Euler and Crank--Nicolson Projection Finite Difference Schemes for Landau--Lifshitz Equation	8
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part II: Optimal Convergence	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
Positivity of Discrete Time-Fractional Operators with Applications to Phase-Field Equations	7
Asymptotically-Preserving Large Deviations Principles by Stochastic Symplectic Methods for a Linear Stochastic Oscillator	7
Error Estimates for Euler Discretization of High-Index Saddle Dynamics	7
Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models	7
Approximating Linear Response by Nonintrusive Shadowing Algorithms	7
Analysis of Error Localization of Chebyshev Spectral Approximations	6
Uniformly Accurate Low Regularity Integrators for the Klein--Gordon Equation from the Classical to NonRelativistic Limit Regime	6

Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version	6
Summation-by-Parts Operators for General Function Spaces	6
Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems	6
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes	6
MINRES for Second-Order PDEs with Singular Data	6
An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation	6
A Variable Time Step Time Filter Algorithm for the Geothermal System	6
On the Sobolev and $L^p$-Stability of the $L^2$-Projection	6
Approximation of Smoothness Classes by Deep Rectifier Networks	6
Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System	6
Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation	6
Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains	6
A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation	6
Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps	6
Low-Rank Updates of Matrix Functions II: Rational Krylov Methods	5
Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems	5
Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem	5
A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm	5
A Narrow-stencil Finite Difference Method for Approximating Viscosity Solutions of Hamilton--Jacobi--Bellman Equations	5
Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides	5
Reciprocal-Log Approximation and Planar PDE Solvers	5
Analysis of Lowest-Order Characteristics-Mixed FEMs for Incompressible Miscible Flow in Porous Media	5
Neural Parametric Fokker--Planck Equation	5
A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation	5
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion	5
Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow	5
An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions	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
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization	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
Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere	5