OOIR: Observatory of International Research

Papers

(The median citation count of Numerical Mathematics-Theory Methods and Applications is 1. 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 2022-06-01 to 2026-06-01.)

Article	Citations
A Generalized Selectively Relaxed Matrix Splitting Preconditioning Strategy for Three-Dimensional Flux-Limited Multi-Group Radiation Diffusion Equations	47
A Priori Error Estimate of Nonconforming Virtual Element Method for Convection Dominated Diffusion Equation	38
Character Modelling with Sketches and ODE-Based Shape Creation	29
Analysis and Optimal Control of a System of Hemivariational Inequalities Arising in Non-Stationary Navier-Stokes Equation with Thermal Effects	26
The Influence of Population Travel Habits on the Spread of Infectious Diseases	16
L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation	14
Space-Time Decomposition of Kalman Filter	12
A Globally Conservative Compact Framework for Conservation Laws: Fourth-Order Schemes with Enhanced Resolution and Stability	11
New Log Basis Functions with a Scaling Factor and Their Applications	9
New Extrapolation Modulus-Based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms	9
Fusing Infrared and Visible Images via a First-Order Model	8
Sparse Deep Neural Network for Nonlinear Partial Differential Equations	8
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field	7
On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations	6
Low Rank and Total Variation Based Two-Phase Method for Image Deblurring with Salt-and-Pepper Impulse Noise	6
Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity	6
Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations	5
Green Function Method for Quantum Transport Based on the Generalized Fourier Transform	4
A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations	4
HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network	4
Implicit-Explicit Time Discretization Schemes for a Class of Semilinear Wave Equations with Nonautonomous Dampings	4
Projection Improved SPAI Preconditioner for FGMRES	4
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations	4
A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes	4
A Novel Semi-Analytical Multiple Invariants-Preserving Integrator for Conservative PDEs	4

Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media	4
A Highly Efficient Adaptive Mesh Refinement Algorithm for the 1D Schr�dinger-Poisson Problem	4
Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series	4
Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains	4
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection	4
Analysis of Deep Ritz Methods for Semilinear Elliptic Equations	4
A Space-Time Extrapolation Cascadic Multigrid Method for 2D Linear Parabolic Problems	4
The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems	3
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations	3
On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion	3
Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model	3
Two Globally Convergent Hybrid CG Methods with Adaptive Restart Strategy for Riemannian Optimization	3
Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation	3
Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model	3
A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels	3
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation	3
A BDF2-SSAV Numerical Scheme with Fourier-Spectral Method for a Droplet Thin Film Coarsening Model	3
A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows	3
A Highly Efficient USOR-Like Iterative Method for the Stationary Wigner Equation with Scattering	2
Entirely Exponential-Type Scheme (E2S) for Optimization Problems with Singularly Perturbed ODE Constraints: The Model Problem	2
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals	2
Convergence Analysis of Split-Douglas-Rachford Algorithm and a Novel Preconditioned ADMM with an Improved Condition	2
A Structure-Preserving JKO Scheme for the Size-Modified Poisson-Nernst-Planck-Cahn-Hilliard Equations	2
Machine Learning-Based Bias Correction for the GEIM Model	2
Density Estimation via Mixture Discrepancy and Moments	2
Convergence Analysis of OT-Flow for Sample Generation	2
Fourier Convergence Analysis for a Fokker-Planck Equation of Tempered Fractional Langevin-Brownian Motion	2
A Modified Version of the PRESB Preconditioner for a Class of Non-Hermitian Complex Systems of Linear Equations	2
Hybrid Difference Scheme for a Coupled Poisson-Schrödinger Equation Modeling Nano Scale Semiconductor Devices: A Singular Perturbation Approach	2
A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis	2
Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations	2
A Stabilized Physics Informed Neural Networks Method for Wave Equations	2
Solving the Helmholtz Equation by Sparse Fundamental Solution Neural Network	2
Two Dynamical Models Based on Projection Operator for Solving the System of Absolute Value Equations Associated with Second-Order Cone	2
An Efficient Variational Model for Multiplicative Noise Removal	2
Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations	1
A Nonlocal Stokes System with Volume Constraints	1
The Relation Between a Tensor and Its Associated Semi-Symmetric Form	1
Analysis and Efficient Implementation of Quadratic Spline Collocation ADI Methods for Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations	1
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation	1
A Moving Mesh Isogeometric Method Based on Harmonic Maps	1
Noise Robust Physics-Informed Generative Adversarial Networks for Solving Stochastic Differential Equations	1
Analysis of Dirichlet-Neumann and Neumann-Dirichlet Methods for Time-Periodic Parabolic Optimal Control Problems	1
Splitting Schemes for Second-Order Backward Stochastic Differential Equations	1
ODE-Based Multistep Schemes for Backward Stochastic Differential Equations	1
A Proximal-Perturbed Bregman ADMM for Solving Nonsmooth and Nonconvex Composite Optimization	1
The Stabilized Finite Element Method for the Cahn-Hilliard Phase-Field Model of Diblock Copolymers on Evolving Surfaces	1
Error Analysis of the Deep Mixed Residual Method for High-Order Elliptic Equations	1
An Asymptotic Preserving Method for the Weakly Nonlinear Klein-Gordon Equation	1
Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation	1

Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator	1
A Divergence-Free $P_k$ CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes	1
The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials	1
A Fast Fully Discrete Mixed Finite Element Scheme for Fractional Viscoelastic Models of Wave Propagation	1
An Extended Courant Element on a Polytope with Application in Approximating an Obstacle Problem	1
Efficiently Training Physics-Informed Neural Networks via Anomaly-Aware Optimization	1
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System	1
The Direct Discontinuous Galerkin Method with Explicit-Implicit-Null Time Discretizations for Nonlinear Diffusion Equations	1
A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model	1
Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem	1
Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations	1
Theoretical Guarantees of Recovery Algorithms for Ternary Sparse Signals	1
Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping	1
Splitting ADI Scheme for Fractional Laplacian Wave Equations	1
Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment	1
Multi-Dimensional Image Recovery via SelfSupervised Nonlinear Transform Based a Three-Directional Tensor Nuclear Norm	1
Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain	1