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 2021-04-01 to 2025-04-01.)

Article	Citations
A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver	33
An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces	14
High-Resolution and High-Precision Weighted Essentially Non-Oscillatory Scheme for Compressible Flow Simulations	13
Superconvergence Error Estimate of the Bilinear-Constant Scheme for the Stokes Equations with Damping	13
Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations	12
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations	11
Oversampled Collocation Approximation Method of Functions via Jacobi Frames	8
Development of a Novel Nonlinear Dynamic Cavitation Model and Its Numerical Validations	7
Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density	7
Stability Analysis for Modelling 3D Poroelastic Wave Propagation by High-Order Staggered-Grid Schemes	7
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations	6
A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrödinger Equation	6
A New Unified Form of Universal Wall Function	6
Static Instability of Ultra-Thin Elastic Structures Using Isogeometric Analysis	5
Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics	5
Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry	5
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography	4
Unified Solution of Conjugate Fluid and Solid Heat Transfer – Part II. High-Order Conjugate Heat Transfer	4
Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method	4
Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model	4
Interaction of Radiation and Turbulent Natural Convection: A Pseudo-Direct Numerical Study	4
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model	4
Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation	3
Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model	3
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes	3

A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms	3
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping	3
Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions	3
Effect of Thermal Convection and Mass Transfer on Particle Motion During Sedimentation: A Numerical Study	3
On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model	3
A Total Variation Based Method for Multivariate Time Series Segmentation	3
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay	3
A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design	3
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems	3
Floating Solid Particles Interacting with Tilted Square Obstacles in Fluid Affecting Drag Forces	3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials	3
Entropy Generation Analysis around Airfoil Using Multi-Block Lattice Boltzmann Method	3
Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles	2
A Hybrid Reconstruction Method Based Upon the Characteristic Fields Decomposition of Compressible Euler Equations	2
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations	2
Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space	2
Edge Detectors Based on Pauta Criterion with Application to Hybrid Compact-WENO Finite Difference Scheme	2
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation	2
Convergence Analysis of a BDF Finite Element Method for the Resistive Magnetohydrodynamic Equations	2
Lattice Boltzmann Method for 2D Tidal Flow: Application to the Nador Lagoon	2
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication	2
Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows	2
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes	2
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models	2
A New Framework of Convergence Analysis for Solving the General Nonlinear Schrödinger Equation Using the Fourier Pseudo-Spectral Method in Two Dimensions	2
Analyzing the Effects of Key Design Factors of a Negative-Differential-Resistance (NDR) Microfluidic Oscillator – An Equivalent-Circuit-Model Approach	2
A Two-Dimensional Thermoelastic Analysis of a Cylindrical Shell Made of FGM with Temperature-Dependent Physical Properties	2
Improvements to Enhance Robustness of Third-Order Scale-Independent WENO-Z Schemes	2
High Order Well-Balanced Finite Difference AWENO Scheme for Ripa and Pollutant Transport Systems	2
A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme	2
A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes	2
Accurate Static and Dynamic Analysis using Unstructured Meshes for Complicated Geometry Problems	2
Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies	2
A Compact Difference Scheme for Time-Space Fractional Nonlinear Diffusion-Wave Equations with Initial Singularity	2
Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem Without Slope Selection	2
A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids	2
Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method	2
A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations	2
Finite Volume Element Method for a Nonlinear Parabolic Equation	2
A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems	2