Numerical Mathematics-Theory Methods and Applications

Article	Citations
A Priori Error Estimate of Nonconforming Virtual Element Method for Convection Dominated Diffusion Equation	32
A Generalized Selectively Relaxed Matrix Splitting Preconditioning Strategy for Three-Dimensional Flux-Limited Multi-Group Radiation Diffusion Equations	28
Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications	21
L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation	21
Analysis and Optimal Control of a System of Hemivariational Inequalities Arising in Non-Stationary Navier-Stokes Equation with Thermal Effects	18
Character Modelling with Sketches and ODE-Based Shape Creation	9
On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations	9
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation	9
New Extrapolation Modulus-based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms	7
New Log Basis Functions with a Scaling Factor and Their Applications	7
Fusing Infrared and Visible Images via a First-Order Model	6
Space-Time Decomposition of Kalman Filter	5
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field	5
Sparse Deep Neural Network for Nonlinear Partial Differential Equations	5
Low Rank and Total Variation Based Two-Phase Method for Image Deblurring with Salt-and-Pepper Impulse Noise	4
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations	4
Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations	4
Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity	4
Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series	3
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection	3
A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes	3
Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains	3
A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations	3
HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network	3
Green Function Method for Quantum Transport Based on the Generalized Fourier Transform	3

The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems	2
A BDF2-SSAV Numerical Scheme with Fourier-Spectral Method for a Droplet Thin Film Coarsening Model	2
Projection Improved SPAI Preconditioner for FGMRES	2
Analysis of Deep Ritz Methods for Semilinear Elliptic Equations	2
Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model	2
A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows	2
Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation	2
Implicit-Explicit Time Discretization Schemes for a Class of Semilinear Wave Equations with Nonautonomous Dampings	2
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations	2
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation	2
Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media	2
On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion	2
Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model	2
Convergence Analysis of OT-Flow for Sample Generation	1
Two Dynamical Models Based on Projection Operator for Solving the System of Absolute Value Equations Associated with Second-Order Cone	1
A Structure-Preserving JKO Scheme for the Size-Modified Poisson-Nernst-Planck-Cahn-Hilliard Equations	1
Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator	1
The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials	1
Splitting ADI Scheme for Fractional Laplacian Wave Equations	1
Noise Robust Physics-Informed Generative Adversarial Networks for Solving Stochastic Differential Equations	1
A Local Deep Learning Method for Solving High Order Partial Differential Equations	1
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals	1
Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations	1
A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels	1
A Divergence-Free $P_k$ CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes	1
The Direct Discontinuous Galerkin Method with Explicit-Implicit-Null Time Discretizations for Nonlinear Diffusion Equations	1
An Efficient Mapped WENO Scheme Using Approximate Constant Mapping	1
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation	1
Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations	1
A Modified Version of the PRESB Preconditioner for a Class of Non-Hermitian Complex Systems of Linear Equations	1
New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model	1
A Stabilized Physics Informed Neural Networks Method for Wave Equations	1
A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis	1
Fourier Convergence Analysis for a Fokker-Planck Equation of Tempered Fractional Langevin-Brownian Motion	1
Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping	1
Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem	1
Analysis and Efficient Implementation of Quadratic Spline Collocation ADI Methods for Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations	1
Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation	1
A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model	1
An Efficient Variational Model for Multiplicative Noise Removal	1
Convergence Analysis of Split-Douglas-Rachford Algorithm and a Novel Preconditioned ADMM with an Improved Condition	1
A Finite Volume Simple WENO Scheme for Convection-Diffusion Equations	0
The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation	0
Solving Generalized Tensor Eigenvalue Problem via Spectral Shifted Inverse Power Methods	0
Greedy Kaczmarz Algorithm Using Optimal Intermediate Projection Technique for Coherent Linear Systems	0
Error Analysis of the Deep Mixed Residual Method for High-Order Elliptic Equations	0
A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds	0
A New Fixed-Time Dynamical System for Absolute Value Equations	0
The Stabilized Finite Element Method for the Cahn-Hilliard Phase-Field Model of Diblock Copolymers on Evolving Surfaces	0
A Physics-Informed Structure-Preserving Numerical Scheme for the Phase-Field Hydrodynamic Model of Ternary Fluid Flows	0

Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations	0
Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations	0
Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain	0
Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations	0
Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes	0
High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids	0
R-Adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-Adaptive Strategy	0
Learning Epidemic Trajectories Through Kernel Operator Learning: From Modelling to Optimal Control	0
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations	0
A Modularized Algorithmic Framework for Interface Related Optimization Problems Using Characteristic Functions	0
Convergence of a Generalized Primal-Dual Algorithm with an Improved Condition for Saddle Point Problems	0
Absorbing Interface Conditions for the Simulation of Wave Propagation on Non-Uniform Meshes	0
An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions	0
Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise	0
The Direct Method of Lines for Forward and Inverse Linear Elasticity Problems of Composite Materials in Star-Shaped Domains	0
An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media	0
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for a Liquid Thin Film Coarsening Model	0
New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications	0
On Lagrange-Projection Schemes for Shallow Water Flows over Movable Bottom with Suspended and Bedload Transport	0
Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes	0
A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product	0
On the Recovery of Source Term for Fractional Evolution PDEs by MC-fPINNs	0
Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers	0
Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations	0
Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations	0
Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D	0
The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems	0
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System	0
On the Criteria for Online Updating of Basis Functions for Model Order Reduction Techniques	0
Finding Cheeger Cuts via 1-Laplacian of Graphs	0
Multi-Dimensional Image Recovery via SelfSupervised Nonlinear Transform Based a Three-Directional Tensor Nuclear Norm	0
A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems	0
An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations	0
An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues	0
Sparse Wavelet Element Method for Piezoelectric Equations in an Unbounded Domain	0
Numerical Integration Formulas for Hypersingular Integrals	0
A Convergence Study of SGD-Type Methods for Stochastic Optimization	0
Non-Local and Fully Connected Tensor Network Decomposition for Remote Sensing Image Denoising	0
Unconditional Convergence of Linearized TL1 Difference Methods for a Time-Fractional Coupled Nonlinear Schrödinger System	0
Geometric Design of Letters in Times Roman Font via RBF Meshless Collocation Method	0
Frontal Slice Approaches for Tensor Linear Systems	0
Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli	0
An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps	0
An Alternating Direction Method of Multipliers for Inverse Lithography Problem	0
A Third-Order Implicit-Explicit Runge-Kutta Method for Landau-Lifshitz Equation with Arbitrary Damping Parameters	0
Artificial Boundary Conditions for Time-Fractional Telegraph Equation	0
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator	0
Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations	0
Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations	0
Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes	0
Error Analysis of the Mixed Residual Method for Elliptic Equations	0
MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs via Monte Carlo Sampling	0
A Stabilizer Free Weak Galerkin Finite Element Method for Elliptic Equation with Lower Regularity	0
A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications	0
A Nonlocal Stokes System with Volume Constraints	0
The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem	0
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes	0
The Relation Between a Tensor and Its Associated Semi-Symmetric Form	0
A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization	0
Variable $s$-Step Technique for New Conjugate Residual Algorithms for Solving Non-Square Linear Systems Arising in Control Problems	0
Convergence Analysis on a Second-Order, Positive, and Unconditional Energy Dissipative Scheme for the Poisson-Nernst-Planck Equations	0
Efficiently Training Physics-Informed Neural Networks via Anomaly-Aware Optimization	0
Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters	0
L1 Schemes for Time-Fractional Differential Equations: A Brief Survey and New Development	0
An Extended Courant Element on a Polytope with Application in Approximating an Obstacle Problem	0
Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems	0
Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations	0
Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-Element in $\mathbb{R}^n$	0
Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment	0
On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method	0
Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates	0
Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport	0
A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation	0
ODE-Based Multistep Schemes for Backward Stochastic Differential Equations	0
Finding Symmetry Groups of Some Quadratic Programming Problems	0
Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems	0
Linearized Double-Shock Approximate Riemann Solver for Augmented Linear Elastic Solid	0
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems	0
Error Analysis for Empirical Risk Minimization over Clipped ReLU Networks in Solving Linear Kolmogorov Partial Differential Equations	0
Numerical Continuation and Bifurcation for Differential Geometric PDEs	0

A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems	0
A Lagrangian Discontinuous Galerkin Scheme for the Compressible Euler Equations on Unstructured Triangular Meshes	0