Advances in Applied Mathematics and Mechanics

Article	Citations
Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation	36
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems	21
On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model	20
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 New Unified Form of Universal Wall Function	16
A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme	16
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations	15
An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations	11
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication	9
An Absolutely Stabilized Virtual Element Method for the Incompressible Stokes Equations	9
A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem	8
Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations	8
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models	8
Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows	8
Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method	8
A First-Order Linear Energy Stable Scheme for the Cahn�Hilliard Equation with Dynamic Boundary Conditions Under the Effect of Hyperbolic Relaxation	7
Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method	7
A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations	7
Unconditionally Energy-Dissipation- and Maximum-Bound-Principle-Preserving Scheme for the Time-Fractional Allen-Cahn Equation	7
Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations	7
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core	7
Weighted Sonine Conditions and Application	7
Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium	6
Troubled-Cell Indicators Using K-Means Clustering for RKDG Methods on Triangular Meshes and $h$-Adaptive Rectangular Meshes	6

Nonlinear Vibroacoustic Analysis of Functionally Graded Plates in the Thermal Ambiance at Oblique Incidence	6
Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation	5
High-Order Unconditionally Energy-Stable Decoupled Method for Phase Field Modeling of Pitting Corrosion with Adaptive Implementation	5
New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws	5
DPK: Deep Neural Network Approximation of the First Piola-Kirchhoff Stress	5
A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem	5
Stability Analysis of Axially Functionally Graded Beams Using the Differential Quadrature Method	5
Two Novel Space-Time Polynomial Particular Solutions Methods for the Time-Dependent Schrödinger Equation	5
A Spectral Split-Step Pad� Method for Guided Wave Propagation	5
Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay	5
Multi-Resolution WENO Method with Adaptive Linear Weights Using Subcell Strategy	5
Explicit, Monotone and Structure-Preserving Finite Difference Methods for Fisher-Kolmogorov-Petrovsky-Piscounov Equation and Allen-Cahn Equation	4
On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime	4
Deep Domain Decomposition Methods: Helmholtz Equation	4
A Fully Discrete Method for Space-Time Fractional Parabolic Problems	4
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint	4
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes	4
A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow	4
Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model	4
Decoupled and Unconditionally Energy Stable Numerical Schemes for the Thermally Coupled Incompressible Magnetohydrodynamics Flow	4
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory	4
Shock Wave Structure of One-Dimensional Hydro-Elastoplastic Riemann Problem with Elastic-Plastic-Fluid Phase Transition	4
Characterizing Natural Convection, Energy, and Thermal Behavior in a Circular Cavity: Finite Element Analysis	4
An Efficient Method for the RCS Reduction of Cavities in the Ground Plane	3
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative	3
Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem	3
Asymptotic Error Analysis for the Discrete Iterated Galerkin Solution of Urysohn Integral Equations with Green’s Kernels	3
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model	3
An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces	3
The Random Feature Method for Elliptic Eigenvalue Problems	3
Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend	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
SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions	3
Stability Analysis for Modelling 3D Poroelastic Wave Propagation by High-Order Staggered-Grid Schemes	3
Application of Lattice Boltzmann Method to Simulate Forest Edge	3
Mass-, and Energy-Preserving Sine Pseudo-Spectral Schemes with High-Accuracy for the Coupled Nonlinear Schrödinger Equation	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	3
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations	3
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials	3
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes	3
Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes	2
Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method	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-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations	2
High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems	2
Strong Converge Order of the General One-Step Method for Neutral Stochastic Delay Differential Equations under a Global Monotone Condition	2
The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering	2
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos	2
Optimizing Thermal Lattice Boltzmann Method on an MT-3000 Processor with Neo-Heterogeneous Strategies	2

Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data	2
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations	2
A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection	2
A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems	2
Finite-Time Stability and Instability of Nonlinear Impulsive Systems	2
Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance	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 Fast Spatial Two-Grid Raviart-Thomas MFE Algorithm for the Nonlinear Time Fractional Diffusion Equations on Temporal Graded Mesh	2
Two Efficient Block Preconditioners for the Mass-Conserved Ohta-Kawasaki Equation	2
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation	2
An Upwind-Block-Centered Multistep Difference Method for a Semiconductor Device and Numerical Analysis	2
The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation	2
An Energy Stable Local Discontinuous Galerkin Method for a Binary Compressible Flow	2
High Order Well-Balanced Finite Difference AWENO Scheme for Ripa and Pollutant Transport Systems	2
Lattice Boltzmann Model for a Class of Viscous Wave Equation	2
Isotropic Cloak Materials Design Based on the Numerical Optimization Method of the Inverse Medium Problem	2
A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows	2
Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions	2
Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics	2
Finite Element Method Coupling Penalty Method for Flexural Shell Model	2
Nonpolynomial Jacobi Spectral-Collocation Method for Weakly Singular Fredholm Integral Equations of the Second Kind	2
Deep Neural Network for Oscillation Dynamics of Capillary Rise	2
A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations	2
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes	2
A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field	2
Postbuckling Analysis of Shear Deformable FGM Cylindrical Shells with Porosities Subjected to Combined Mechanical Loads in Thermal Environments	1
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography	1
An Explicit Superconvergent Weak Galerkin Finite Element Method for the Heat Equation	1
Superconvergence Error Estimate of the Bilinear-Constant Scheme for the Stokes Equations with Damping	1
Parallel Domain Decomposition-Based Solver for the Simulation of Flow over an Ahmed Reference Model	1
Improved Sixth-Order WENO Finite Difference Schemes for Hyperbolic Conservation Laws	1
The Formulation of Finite Difference Hermite RBF-WENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique	1
Characterising Mechanical Properties of Flowing Microcapsules Using a Deep Convolutional Neural Network	1
A Conservative Sharp Interface Method for Compressible Two-Medium Flows on Unstructured Triangular Meshes	1
Adaptive Finite Element Solutions of a Diffusion Model for Drug Release in PLGA Microspheres	1
A Modified Regularized Lattice Boltzmann Method for Coupled Thermal-Solutal Problems of Non-Newtonian Fluids in Heterogeneously Porous Media	1
Investigating Droplet and Bubble Deformation under Shear Flow Using the Multi-Pseudo-Potential Scheme of Lattice Boltzmann Method	1
A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy	1
Cell-Average Based Neural Network Method for Hunter-Saxton Equations	1
PINN-Based Partial Learning for Multicontinuum Problems: Dual Continuum Fluid Filtration Simulation	1
Impact Dynamics of Binary Off-Center Unequal-Sized Droplets Colliding on a Superhydrophobic Surface	1
High-Order Numerical Approximation and Error Estimation for Fourth-Order Equation in Complex Cylindrical Domain	1
Spectral Scheme for Nonlinear Volterra Integro-Differential Equation	1
A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver	1
Fluid-Structure Interactions: One-Field Monolithic Fictitious Domain Method and Its Parallelization	1
Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space	1
Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method	1
Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles	1
Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density	1
Interaction of Radiation and Turbulent Natural Convection: A Pseudo-Direct Numerical Study	1
Free Vibration of Stiffened Plate with Cracked Stiffeners	1
Floating Solid Particles Interacting with Tilted Square Obstacles in Fluid Affecting Drag Forces	1
A Mass-Preserving Characteristic Finite Difference Method for Miscible Displacement Problem	1
A Reconstructed Discontinuous Approximation to Monge-Ampère Equation in Least Square Formulation	1
A Boundary Mapped Collocation Method for the Analysis of the Arbitrarily Shaped Plates	1
First-Order, Unconditionally Stable, Fully Decoupled Methods for the Penalty Ericksen-Leslie System with Variable Density	1
Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with $Φ_p$ Operator and Mittag-Leffler Kernel	1
A Modified Hybrid High-Order Essentially Non-Oscillatory Compact Difference Scheme for Nonlinear Degenerate Parabolic Equations	1
The Boundary Mapped Collocation Method for Heat Conduction Problems with Heat Generation Spatially Varying Conductivity	1
Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions	1
A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes	1
Convergence Analysis of a BDF Finite Element Method for the Resistive Magnetohydrodynamic Equations	1
A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems	1
Critical Transition Reynolds Number for the Incompressible Flat-Plate Boundary Layer as Searched by Numerical Simulation	1
Unified Solution of Conjugate Fluid and Solid Heat Transfer – Part II. High-Order Conjugate Heat Transfer	1
High-Efficiency Explicit Multistep Schemes for Coupled Second-Order FBSDEs	1
Numerical Investigation of Dynamics Stall on Vertical Axis Wind Turbine	1
A Fast Cascadic Multigrid Method for Direct Finite Difference Discretizations of 3D Biharmonic Equations on Rectangular Domains	1
Mechanisms for Stabilizing Thermal Lattice Boltzmann Equation and Their Applications for Convection-Diffusion Problem on Nonuniform Meshes	1
A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer	1
High-Resolution and High-Precision Weighted Essentially Non-Oscillatory Scheme for Compressible Flow Simulations	1
A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model	1
The Generalized Riemann Problem for Two-Layer Shallow Water Equations with Two-Velocities	1
Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem	1
Development of a Novel Nonlinear Dynamic Cavitation Model and Its Numerical Validations	1
Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method	1
HAM-Schrödingerisation: A Generic Framework of Quantum Simulation for Any Nonlinear PDEs	1
Optimal Error Analysis of Euler and BDF2 Semi-Renormalized FEMs for the Landau-Lifshitz-Slonczewski Equation	1
Taylor Remainder-Based Discontinuity Detection Method with Application to Hybrid Compact-WENO Finite Difference Scheme for Hyperbolic Conservation Laws	1
On Stable Difference Schemes for the Solution of Soliton Type Coupled Sine-Gordon Equations in the Weak Sense	1

Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity	1
A Three-Dimensional Mass-Conserved Multiphase Lattice Boltzmann Flux Solver for Incompressible Flows with Large Density and Viscosity Ratios	1
A Novel Temporal Two-Grid Compact Finite Difference Scheme for the Viscous Burgers’ Equation	1
A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images	1
Static Instability of Ultra-Thin Elastic Structures Using Isogeometric Analysis	1
A Scale-Invariant Fifth Order WCNS Scheme for Hyperbolic Conservation Laws	1
Ultraspherical Spectral Method for Block Copolymer Systems on Unit Disk	1
A New Composite Wall Function for Adverse Pressure Gradient Flows	1
Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations	1
A CDM-Based Tensile Instability Analysis in DP1180 Steel Sheet	1
The Investigation of Rayleigh-Taylor Mixing with a Premixed Layer by BHR Turbulence Model	1