OOIR: Observatory of International Research

Papers

(The TQCC of Advances in Applied Mathematics and Mechanics is 2. 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 2022-08-01 to 2026-08-01.)

Article	Citations
Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation	21
Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry	20
Oversampled Collocation Approximation Method of Functions via Jacobi Frames	17
A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme	17
An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations	10
An Absolutely Stabilized Virtual Element Method for the Incompressible Stokes Equations	9
A New Unified Form of Universal Wall Function	8
On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model	8
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations	7
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models	7
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems	7
Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows	7
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core	6
A First-Order Linear Energy Stable Scheme for the Cahn–Hilliard Equation with Dynamic Boundary Conditions Under the Effect of Hyperbolic Relaxation	6
Weighted Sonine Conditions and Application	6
A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations	6
Multi-Subband Transfer Matrix Method for the Two-Dimensional Schrödinger Equation in Quantum Devices	6
Nonlinear Vibroacoustic Analysis of Functionally Graded Plates in the Thermal Ambiance at Oblique Incidence	5
Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations	5
Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay	5
Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method	5
Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations	5
Unconditionally Energy-Dissipation- and Maximum-Bound-Principle-Preserving Scheme for the Time-Fractional Allen-Cahn Equation	5
High-Order Unconditionally Energy-Stable Decoupled Method for Phase Field Modeling of Pitting Corrosion with Adaptive Implementation	4
A Spectral Split-Step Padé Method for Guided Wave Propagation	4

On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime	4
Multi-Resolution WENO Method with Adaptive Linear Weights Using Subcell Strategy	4
Troubled-Cell Indicators Using K-Means Clustering for RKDG Methods on Triangular Meshes and $h$-Adaptive Rectangular Meshes	4
Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method	4
New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws	4
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes	4
DPK: Deep Neural Network Approximation of the First Piola-Kirchhoff Stress	4
A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem	4
Stability Analysis of Axially Functionally Graded Beams Using the Differential Quadrature Method	4
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory	4
Two Novel Space-Time Polynomial Particular Solutions Methods for the Time-Dependent Schrödinger Equation	4
Explicit, Monotone and Structure-Preserving Finite Difference Methods for Fisher-Kolmogorov-Petrovsky-Piscounov Equation and Allen-Cahn Equation	3
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative	3
Shock Wave Structure of One-Dimensional Hydro-Elastoplastic Riemann Problem with Elastic-Plastic-Fluid Phase Transition	3
The Random Feature Method for Elliptic Eigenvalue Problems	3
A Robust Three-Level Time Split High-Order Leapfrog/Crank-Nicolson Scheme for Two-Dimensional Sobolev and Regularized Long Wave Equations Arising in Fluid Mechanics	3
Deep Domain Decomposition Methods: Helmholtz Equation	3
Decoupled and Unconditionally Energy Stable Numerical Schemes for the Thermally Coupled Incompressible Magnetohydrodynamics Flow	3
A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow	3
Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model	3
A Fully Discrete Method for Space-Time Fractional Parabolic Problems	3
Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem	3
An Efficient Method for the RCS Reduction of Cavities in the Ground Plane	3
Characterizing Natural Convection, Energy, and Thermal Behavior in a Circular Cavity: Finite Element Analysis	3
A Ciarlet-Raviart Mixed Finite Element Method for Optimal Control Problems Governed by a Fourth Order Bi-Wave Equation	3
Corrected Linear-Galerkin Schemes to Preserve Second-Order Accuracy for Cell-Centered Unstructured Finite Volume Methods	2
Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions	2
Mass-, and Energy-Preserving Sine Pseudo-Spectral Schemes with High-Accuracy for the Coupled Nonlinear Schrödinger Equation	2
A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems	2
The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering	2
Strong Converge Order of the General One-Step Method for Neutral Stochastic Delay Differential Equations under a Global Monotone Condition	2
High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems	2
Stability Analysis for Modelling 3D Poroelastic Wave Propagation by High-Order Staggered-Grid Schemes	2
Conservative Three-Level Linearized Finite Difference Schemes for the Rosenau-KdV Equation	2
Buckling Analysis of Functionally Graded Beams under Combined Loadings	2
Optimizing Thermal Lattice Boltzmann Method on an MT-3000 Processor with Neo-Heterogeneous Strategies	2
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials	2
Asymptotic Error Analysis for the Discrete Iterated Galerkin Solution of Urysohn Integral Equations with Green’s Kernels	2
Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics	2
Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations	2
Power Series Solution and Its Indirect Precision Evaluation of Camassa–Holm Equation	2
Fully Discrete Schemes with First- and Second-Order Temporal Accuracy for the Incompressible Magnetohydrodynamic Flow Based on the Generalized Scalar Auxiliary Variable Approach	2
A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows	2
Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance	2
A New Framework of Convergence Analysis for Solving the General Nonlinear Schrödinger Equation Using the Fourier Pseudo-Spectral Method in Two Dimensions	2
Two Efficient Block Preconditioners for the Mass-Conserved Ohta-Kawasaki Equation	2
An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces	2
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations	2
SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions	2
Application of Lattice Boltzmann Method to Simulate Forest Edge	2

High Order Well-Balanced Finite Difference AWENO Scheme for Ripa and Pollutant Transport Systems	2
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes	2
Evaluation of Geothermal Energy Extraction in Enhanced Geothermal System (EGS) with Multiple Stage Fracturing Wells (MSFW)	2
A Fast Spatial Two-Grid Raviart-Thomas MFE Algorithm for the Nonlinear Time Fractional Diffusion Equations on Temporal Graded Mesh	2
Deep Neural Network for Oscillation Dynamics of Capillary Rise	2
The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation	2
A Robust Weighted Compact Nonlinear Scheme for Compressible Euler Equations	2
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes	2
Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend	2