Advances in Applied Mathematics and Mechanics

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 2021-08-01 to 2025-08-01.)
ArticleCitations
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations35
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems19
An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations17
Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model17
Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation17
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication13
Oversampled Collocation Approximation Method of Functions via Jacobi Frames9
Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry9
A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme8
A New Unified Form of Universal Wall Function8
On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model8
Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations7
Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method7
A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations7
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core6
A Cell-Centered Lagrangian Scheme with an Elastic-Perfectly Plastic Solid Riemann Solver for Wave Propagations in Solids6
Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows6
Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium5
A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem5
Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation5
Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies5
Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations5
Troubled-Cell Indicators Using K-Means Clustering for RKDG Methods on Triangular Meshes and $h$-Adaptive Rectangular Meshes5
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models5
A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem4
On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime4
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes4
Nonlinear Vibroacoustic Analysis of Functionally Graded Plates in the Thermal Ambiance at Oblique Incidence4
Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method4
DPK: Deep Neural Network Approximation of the First Piola-Kirchhoff Stress4
Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay4
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory4
Stability Analysis of Axially Functionally Graded Beams Using the Differential Quadrature Method4
New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws3
An Efficient Method for the RCS Reduction of Cavities in the Ground Plane3
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials3
Application of Lattice Boltzmann Method to Simulate Forest Edge3
The Random Feature Method for Elliptic Eigenvalue Problems3
Deep Domain Decomposition Methods: Helmholtz Equation3
Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model3
SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions3
Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem3
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint3
Shock Wave Structure of One-Dimensional Hydro-Elastoplastic Riemann Problem with Elastic-Plastic-Fluid Phase Transition3
A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow3
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative3
Asymptotic Error Analysis for the Discrete Iterated Galerkin Solution of Urysohn Integral Equations with Green’s Kernels3
The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering2
Deep Neural Network for Oscillation Dynamics of Capillary Rise2
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations2
Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions2
An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces2
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations2
Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend2
High Order Well-Balanced Finite Difference AWENO Scheme for Ripa and Pollutant Transport Systems2
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes2
Finite Element Method Coupling Penalty Method for Flexural Shell Model2
Isotropic Cloak Materials Design Based on the Numerical Optimization Method of the Inverse Medium Problem2
High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems2
A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows2
The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation2
A New Framework of Convergence Analysis for Solving the General Nonlinear Schrödinger Equation Using the Fourier Pseudo-Spectral Method in Two Dimensions2
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay2
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model2
Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations2
A Robust Three-Level Time Split High-Order Leapfrog/Crank-Nicolson Scheme for Two-Dimensional Sobolev and Regularized Long Wave Equations Arising in Fluid Mechanics2
Lattice Boltzmann Model for a Class of Viscous Wave Equation2
Fully Discrete Schemes with First- and Second-Order Temporal Accuracy for the Incompressible Magnetohydrodynamic Flow Based on the Generalized Scalar Auxiliary Variable Approach2
Two Efficient Block Preconditioners for the Mass-Conserved Ohta-Kawasaki Equation2
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation2
Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics2
Stability Analysis for Modelling 3D Poroelastic Wave Propagation by High-Order Staggered-Grid Schemes2
Mass-, and Energy-Preserving Sine Pseudo-Spectral Schemes with High-Accuracy for the Coupled Nonlinear Schrödinger Equation2
Corrected Linear-Galerkin Schemes to Preserve Second-Order Accuracy for Cell-Centered Unstructured Finite Volume Methods2
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes2
Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance2
Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes2
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