SIAM Journal on Numerical Analysis

Article	Citations
Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Convergence Analysis	34
High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation	27
Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field	25
A General Framework of Low Regularity Integrators	24
A Structure-Preserving Parametric Finite Element Method for Surface Diffusion	23
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows	22
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case	21
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis	21
An Artificial Compressibility Crank--Nicolson Leap-Frog Method for the Stokes--Darcy Model and Application in Ensemble Simulations	20
Computational Methods for First-Order Nonlocal Mean Field Games with Applications	19
Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights	19
Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers	18
Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data	18
Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences	18
Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations	18
Time Integration of Tree Tensor Networks	16
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion	16
Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance	16
Discovery of Dynamics Using Linear Multistep Methods	15
Local Energy Estimates for the Fractional Laplacian	15
Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows	15
Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization	14
Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit	14
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions	14
Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems	13

Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier--Stokes Equations with Periodic Boundary Conditions	13
A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients	13
Approximation of High-Dimensional Periodic Functions with Fourier-Based Methods	13
An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws	13
Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations	12
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties	12
A Family of Finite Element Stokes Complexes in Three Dimensions	12
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition	12
A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation	12
Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity	12
A Unified Convergence Analysis for the Fractional Diffusion Equation Driven by Fractional Gaussian Noise with Hurst Index $H\in(0,1)$	11
Error Estimates for the Optimal Control of a Parabolic Fractional PDE	11
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem	11
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving	11
Strong Convergence of Full Discretization for Stochastic Cahn--Hilliard Equation Driven by Additive Noise	11
Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates	10
The Energy Technique for the Six-Step BDF Method	10
Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization	10
Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements	10
Temporal Second-Order Finite Difference Schemes for Variable-Order Time-Fractional Wave Equations	10
Divergence-free Scott--Vogelius Elements on Curved Domains	10
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems	9
Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities	9
The Connections Between Lyapunov Functions for Some Optimization Algorithms and Differential Equations	9
\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension	9
Modeling and Analysis of the Coupling in Discrete Fracture Matrix Models	9
Carleman-Based Reconstruction Algorithm for Waves	9
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion	9
A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics	9
On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization	9
Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential	9
Finite Elements for div- and divdiv-Conforming Symmetric Tensors in Arbitrary Dimension	8
Optimal Error Analysis of Euler and Crank--Nicolson Projection Finite Difference Schemes for Landau--Lifshitz Equation	8
Locking-Free Enriched Galerkin Method for Linear Elasticity	8
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property	8
Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations	8
Rank-Adaptive Time Integration of Tree Tensor Networks	8
Computing Semigroups with Error Control	8
Positivity of Discrete Time-Fractional Operators with Applications to Phase-Field Equations	7
Asymptotically-Preserving Large Deviations Principles by Stochastic Symplectic Methods for a Linear Stochastic Oscillator	7
Error Estimates for Euler Discretization of High-Index Saddle Dynamics	7
Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models	7
Approximating Linear Response by Nonintrusive Shadowing Algorithms	7
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part II: Optimal Convergence	7
Local Convergence of the FEM for the Integral Fractional Laplacian	7
Hybrid Localized Spectral Decomposition for Multiscale Problems	7
Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part I: Uniform Stability	7
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation	7
Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System	6
Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation	6

Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains	6
A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation	6
Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps	6
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes	6
Analysis of Error Localization of Chebyshev Spectral Approximations	6
Uniformly Accurate Low Regularity Integrators for the Klein--Gordon Equation from the Classical to NonRelativistic Limit Regime	6
Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version	6
Summation-by-Parts Operators for General Function Spaces	6
Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems	6
MINRES for Second-Order PDEs with Singular Data	6
An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation	6
A Variable Time Step Time Filter Algorithm for the Geothermal System	6
On the Sobolev and $L^p$-Stability of the $L^2$-Projection	6
Approximation of Smoothness Classes by Deep Rectifier Networks	6
Convergence in Total Variation of the Euler--Maruyama Scheme Applied to Diffusion Processes with Measurable Drift Coefficient and Additive Noise	5
Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere	5
Low-Rank Updates of Matrix Functions II: Rational Krylov Methods	5
Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems	5
Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem	5
A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm	5
A Narrow-stencil Finite Difference Method for Approximating Viscosity Solutions of Hamilton--Jacobi--Bellman Equations	5
Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides	5
Reciprocal-Log Approximation and Planar PDE Solvers	5
Analysis of Lowest-Order Characteristics-Mixed FEMs for Incompressible Miscible Flow in Porous Media	5
Neural Parametric Fokker--Planck Equation	5
A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation	5
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion	5
Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow	5
An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions	5
A Polynomial-Degree-Robust A Posteriori Error Estimator for Nédélec Discretizations of Magnetostatic Problems	5
Improving Accuracy of the Fifth-Order WENO Scheme by Using the Exponential Approximation Space	5
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization	5
A Fourth-Order Unfitted Characteristic Finite Element Method for Solving the Advection-Diffusion Equation on Time-Varying Domains	5
Convergence Analysis of Discrete High-Index Saddle Dynamics	4
Error Estimate of Unconditionally Stable and Decoupled Linear Positivity-Preserving FEM for the Chemotaxis-Stokes Equations	4
An Energy Stable and Positivity-Preserving Scheme for the Maxwell--Stefan Diffusion System	4
Analysis and Approximations of Dirichlet Boundary Control of Stokes Flows in the Energy Space	4
Error Localization of Best $L_{1}$ Polynomial Approximants	4
Hypocoercivity-compatible Finite Element Methods for the Long-time Computation of Kolmogorov's Equation	4
Stability of Variable-Step BDF2 and BDF3 Methods	4
Strong Convergence of a Verlet Integrator for the Semilinear Stochastic Wave Equation	4
A Semi-implicit Exponential Low-Regularity Integrator for the Navier--Stokes Equations	4
A Symplectic Discontinuous Galerkin Full Discretization for Stochastic Maxwell Equations	4
A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed Curves	4
Efficient Approximation of SDEs Driven by Countably Dimensional Wiener Process and Poisson Random Measure	4
Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations	4
Fractional Semilinear Optimal Control: Optimality Conditions, Convergence, and Error Analysis	4
Convergence Rate of Markov Chains and Hybrid Numerical Schemes to Jump-Diffusion with Application to the Bates Model	4
A Convergent Structure-Preserving Finite-Volume Scheme for the Shigesada--Kawasaki--Teramoto Population System	4
Space-Time Approximation of Stochastic $p$-Laplace-Type Systems	4
A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation	3
Stability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP Property	3
Coupling Parareal with Optimized Schwarz Waveform Relaxation for Parabolic Problems	3
Computation of the Complex Error Function Using Modified Trapezoidal Rules	3
On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems	3
Flux-Mortar Mixed Finite Element Methods on NonMatching Grids	3
Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues	3
Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness	3
Sinc-$\theta$ Schemes for Backward Stochastic Differential Equations	3
Convergence Analysis of Pixel-Driven Radon and Fanbeam Transforms	3
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems	3
Adaptive Mixed Finite Element Methods for Non-self-adjoint Indefinite Second-Order Elliptic PDEs with Optimal Rates	3
Full Discretization of Cauchy's Problem by Lavrentiev--Finite Element Method	3
A Local Discontinuous Galerkin Approximation for the p-Navier–Stokes System, Part I: Convergence Analysis	3
On the Infinite Order Limit of Hermite-based Finite Difference Schemes	3
A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning	3
$L^\infty$ Norm Error Estimates for HDG Methods Applied to the Poisson Equation with an Application to the Dirichlet Boundary Control Problem	3
A $C^1$ Conforming Petrov--Galerkin Method for Convection-Diffusion Equations and Superconvergence Analysis over Rectangular Meshes	3
Identification of Potential in Diffusion Equations from Terminal Observation: Analysis and Discrete Approximation	3
A Mixed Approach to the Poisson Problem with Line Sources	3
Error Analysis of Energy-Preserving Mixed Finite Element Methods for the Hodge Wave Equation	3
Erratum: Convergence of Dziuk’s Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-Order Finite Elements	3
Stratified Radiative Transfer in a Fluid and Numerical Applications to Earth Science	3
Well-Posedness and Convergence of a Finite Volume Method for Conservation Laws on Networks	3
A Priori Error Analysis of a Numerical Stochastic Homogenization Method	3
On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field	3
Convergence of a Second-order Energy-decaying Method for the Viscous Rotating Shallow Water Equation	3
On the Finite Element Approximation of a Semicoercive Stokes Variational Inequality Arising in Glaciology	3
On the Convergence of Discontinuous Galerkin/Hermite Spectral Methods for the Vlasov–Poisson System	3
Fluid-Fluid Interaction Problems at High Reynolds Numbers: Reducing the Modeling Error with LES-C	3

Optimized Transmission Conditions in Domain Decomposition Methods with Cross-Points for Helmholtz Equation	3
Optimization and Convergence of Numerical Attractors for Discrete-Time Quasi-Linear Lattice System	3
Adaptive Multilevel Monte Carlo for Probabilities	3
A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces	3
Value-Gradient Based Formulation of Optimal Control Problem and Machine Learning Algorithm	2
Numerical Analysis for Maxwell Obstacle Problems in Electric Shielding	2
Continuous Time Limit of the Stochastic Ensemble Kalman Inversion: Strong Convergence Analysis	2
Fast Krasnosel’skiĭ–Mann Algorithm with a Convergence Rate of the Fixed Point Iteration of \(\boldsymbol{{ o} \left(\frac{1}{{ k}} \right)}\)	2
Optimal \(\boldsymbol{{L^2}}\) Error Estimates of Unconditionally Stable Finite Element Schemes for the Cahn–Hilliard–Navier–Stokes System	2
Error Analysis for Probabilities of Rare Events with Approximate Models	2
Summation-by-Parts Approximations of the Second Derivative: Pseudoinverse and Revisitation of a High Order Accurate Operator	2
A Convergent Interacting Particle Method and Computation of KPP Front Speeds in Chaotic Flows	2
A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity	2
A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg–de Vries Equation	2
An Exponential Spectral Method Using VP Means for Semilinear Subdiffusion Equations with Rough Data	2
Frequency-Explicit A Posteriori Error Estimates for Finite Element Discretizations of Maxwell's Equations	2
Direct Guaranteed Lower Eigenvalue Bounds with Optimal a Priori Convergence Rates for the Bi-Laplacian	2
Strong Convergence Order for the Scheme of Fractional Diffusion Equation Driven by Fractional Gaussian Noise	2
Gauge-Transformed Exponential Integrator for Generalized KdV Equations with Rough Data	2
Agglomeration-Based Geometric Multigrid Schemes for the Virtual Element Method	2
Finite Element Method for a Nonlinear Perfectly Matched Layer Helmholtz Equation with High Wave Number	2
Approximation from Noisy Data	2
An Improved High-Order Method for Elliptic Multiscale Problems	2
Analysis and Application of Two Novel Finite Element Methods for Solving Ziolkowski’s PML Model in the Integro-Differential Form	2
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems	2
Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems	2
A Monolithic Divergence-Conforming HDG Scheme for a Linear Fluid-Structure Interaction Model	2
Error Analysis for a Finite Difference Scheme for Axisymmetric Mean Curvature Flow of Genus-0 Surfaces	2
The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations	2
POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution	2
Computational Lower Bounds of the Maxwell Eigenvalues	2
Accuracy of Spectral Element Method for Wave, Parabolic, and Schrödinger Equations	2
The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method	2
Convergence Analysis of a Fully Discrete Energy-Stable Numerical Scheme for the Q-Tensor Flow of Liquid Crystals	2
Convergence Analysis of Inexact Two-Grid Methods: A Theoretical Framework	2
Convergence of a Decoupled Splitting Scheme for the Cahn–Hilliard–Navier–Stokes System	2
A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations	2
A Complex Homographic Best Approximation Problem. Application to Optimized Robin--Schwarz Algorithms, and Optimal Control Problems	2
Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material	2
\({\boldsymbol{H^1}}\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation	2
Taylor--Hood Discretization of the Reissner--Mindlin Plate	2
A Posteriori Error Analysis of the inf-sup Constant for the Divergence	2
Optimal Maximum Norm Estimates for Virtual Element Methods	2
A Class of Boundary Conditions for Time-Discrete Green--Naghdi Equations with Bathymetry	2
From Additive Average Schwarz Methods to Nonoverlapping Spectral Additive Schwarz Methods	2
A Rigorous Numerical Analysis of the Transformed Field Expansion Method for Diffraction by Periodic, Layered Structures	2
A Convexity-Preserving and Perimeter-Decreasing Parametric Finite Element Method for the Area-Preserving Curve Shortening Flow	2
Optimal Analysis of Non-Uniform Galerkin-Mixed Finite Element Approximations to the Ginzburg–Landau Equations in Superconductivity	2
Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion	2
A Numerical Energy Reduction Approach for Semilinear Diffusion-Reaction Boundary Value Problems Based on Steady-State Iterations	2
L$^2$ Error Estimate to Smooth Solutions of High Order Runge--Kutta Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws with and without Sonic Points	2
On the Convergence to Local Limit of Nonlocal Models with Approximated Interaction Neighborhoods	2
A Posteriori Estimates for the Stochastic Total Variation Flow	2
Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners	2
Stein Variational Gradient Descent on Infinite-Dimensional Space and Applications to Statistical Inverse Problems	2
Second-Order Accurate TVD Numerical Methods for Nonlocal Nonlinear Conservation Laws	2
Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems	2
Ensemble Domain Decomposition Algorithm for the Fully Mixed Random Stokes–Darcy Model with the Beavers–Joseph Interface Conditions	2