Advances in Applied Mathematics and Mechanics

Papers
(The TQCC of Advances in Applied Mathematics and Mechanics 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 2021-02-01 to 2025-02-01.)
ArticleCitations
A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver33
An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces14
Superconvergence Error Estimate of the Bilinear-Constant Scheme for the Stokes Equations with Damping13
High-Resolution and High-Precision Weighted Essentially Non-Oscillatory Scheme for Compressible Flow Simulations13
Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations12
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations9
Oversampled Collocation Approximation Method of Functions via Jacobi Frames8
Stability Analysis for Modelling 3D Poroelastic Wave Propagation by High-Order Staggered-Grid Schemes7
Development of a Novel Nonlinear Dynamic Cavitation Model and Its Numerical Validations7
A New Unified Form of Universal Wall Function6
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations6
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model6
Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density6
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography5
Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model5
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes4
Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method4
On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model4
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems4
Interaction of Radiation and Turbulent Natural Convection: A Pseudo-Direct Numerical Study4
A Total Variation Based Method for Multivariate Time Series Segmentation4
Effect of Thermal Convection and Mass Transfer on Particle Motion During Sedimentation: A Numerical Study4
Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model3
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication3
A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems3
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials3
A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms3
A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrödinger Equation3
Entropy Generation Analysis around Airfoil Using Multi-Block Lattice Boltzmann Method3
Floating Solid Particles Interacting with Tilted Square Obstacles in Fluid Affecting Drag Forces3
Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation3
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay3
Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions3
A Hybrid Reconstruction Method Based Upon the Characteristic Fields Decomposition of Compressible Euler Equations2
Improvements to Enhance Robustness of Third-Order Scale-Independent WENO-Z Schemes2
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation2
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations2
Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies2
A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations2
Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics2
Static Instability of Ultra-Thin Elastic Structures using Isogeometric Analysis2
High Order Well-Balanced Finite Difference AWENO Scheme for Ripa and Pollutant Transport Systems2
Unified Solution of Conjugate Fluid and Solid Heat Transfer--Part II. High-Order Conjugate Heat Transfer2
Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method2
A Two-Dimensional Thermoelastic Analysis of a Cylindrical Shell Made of FGM with Temperature-Dependent Physical Properties2
Lattice Boltzmann Method for 2D Tidal Flow: Application to the Nador Lagoon2
Convergence Analysis of a BDF Finite Element Method for the Resistive Magnetohydrodynamic Equations2
Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry2
Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles2
A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme2
Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows2
A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids2
Analyzing the Effects of Key Design Factors of a Negative-Differential-Resistance (NDR) Microfluidic Oscillator – An Equivalent-Circuit-Model Approach2
Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions2
Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations2
A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes2
A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design2
The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation1
Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations1
Finite Volume Element Method for a Nonlinear Parabolic Equation1
A New Well-Balanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography1
Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion1
A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem1
High Order Efficient Algorithm for Computation of MHD Flow Ensembles1
Critical Transition Reynolds Number for the Incompressible Flat-Plate Boundary Layer as Searched by Numerical Simulation1
Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method1
A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation1
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models1
A New Framework of Convergence Analysis for Solving the General Nonlinear Schrödinger Equation Using the Fourier Pseudo-Spectral Method in Two Dimensions1
Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem Without Slope Selection1
Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity1
The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations1
A Buckley-Leverett Theory Based Lattice Boltzmann Method for Immiscible Two-Phase Flow with Viscous Coupling in Porous Media1
A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images1
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core1
A Scale-Invariant Fifth Order WCNS Scheme for Hyperbolic Conservation Laws1
Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space1
Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations1
A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids1
An Isoparametric Finite Element Method for Reissner-Mindlin Plate Problem on Curved Domain1
Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions1
Convergence and Stability of an Explicit Method for Autonomous Time-Changed Stochastic Differential Equations with Super-Linear Coefficients1
Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm1
Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel1
An Efficient Regularized Lattice Boltzmann Method to Solve Consistent and Conservative Phase Field Model for Simulating Incompressible Two-Phase Flows1
A Second-Order Alikhanov Type Implicit Scheme for the Time-Space Fractional Ginzburg-Landau Equation1
Cell-Average Based Neural Network Method for Hunter-Saxton Equations1
Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory1
Modified Galerkin Method for Derivative Dependent Fredholm–Hammerstein Integral Equations of Second Kind1
A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model1
A Compact Difference Scheme for Time-Space Fractional Nonlinear Diffusion-Wave Equations with Initial Singularity1
Finite Element Method Coupling Penalty Method for Flexural Shell Model1
The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems1
Investigating Droplet and Bubble Deformation under Shear Flow Using the Multi-Pseudo-Potential Scheme of Lattice Boltzmann Method1
The Boundary Mapped Collocation Method for Heat Conduction Problems with Heat Generation Spatially Varying Conductivity1
A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem1
Edge Detectors Based on Pauta Criterion with Application to Hybrid Compact-WENO Finite Difference Scheme1
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes1
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