OOIR: Observatory of International Research

Papers

(The TQCC of SIAM Journal on Numerical Analysis is 4. 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 2021-03-01 to 2025-03-01.)

Article	Citations
Geometric Ergodicity for Hamiltonian Monte Carlo on Compact Manifolds	40
An Optimal Mass Transport Method for Random Genetic Drift	28
Orthogonal Polynomial Approximation and Extended Dynamic Mode Decomposition in Chaos	23
Cut Finite Element Method for Divergence-Free Approximation of Incompressible Flow: A Lagrange Multiplier Approach	21
Full-Spectrum Dispersion Relation Preserving Summation-by-Parts Operators	21
Numerical Reconstruction of Diffusion and Potential Coefficients from Two Observations: Decoupled Recovery and Error Estimates	20
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation	19
On the Superconvergence of a Hybridizable Discontinuous Galerkin Method for the Cahn–Hilliard Equation	17
Solving PDEs with Incomplete Information	17
Convergence Analysis of Leapfrog for Geodesics	16
A Robust Lower-Order Mixed Finite Element Method for a Strain Gradient Elastic Model	16
Analysis and Application of Two Novel Finite Element Methods for Solving Ziolkowski’s PML Model in the Integro-Differential Form	15
An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model	15
Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems	13
A Novel Mixed Spectral Method and Error Estimates for Maxwell Transmission Eigenvalue Problems	13
Density Estimation in RKHS with Application to Korobov Spaces in High Dimensions	13
Continuous Time Limit of the Stochastic Ensemble Kalman Inversion: Strong Convergence Analysis	12
Randomized Least-Squares with Minimal Oversampling and Interpolation in General Spaces	12
A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm	12
Approximations of Energy Minimization in Cell-Induced Phase Transitions of Fibrous Biomaterials: $\Gamma$-Convergence Analysis	12
Generalized Dimension Truncation Error Analysis for High-Dimensional Numerical Integration: Lognormal Setting and Beyond	10
A Local Discontinuous Galerkin Approximation for thep-Navier–Stokes System, Part I: Convergence Analysis	10
Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation	10
Spectral Analysis of a Mixed Method for Linear Elasticity	10
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion	10

High Order Biorthogonal Functions in ${H}$(curl)	10
${H^m}$-Conforming Virtual Elements in Arbitrary Dimension	10
A Local Discontinuous Galerkin Approximation for the $\boldsymbol{{p}}$ -Navier–Stokes System, Part II: Convergence Rates for the Velocity	9
Sparse Monte Carlo Method for Nonlocal Diffusion Problems	9
Efficient Approximation of SDEs Driven by Countably Dimensional Wiener Process and Poisson Random Measure	9
Local Convergence of the FEM for the Integral Fractional Laplacian	9
On the Finite Element Approximation of a Semicoercive Stokes Variational Inequality Arising in Glaciology	9
Nonlinear Eigenvalue Methods for Linear Pointwise Stability of Nonlinear Waves	8
Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model	8
Exponential Convergence of $hp$-FEM for the Integral Fractional Laplacian in Polygons	8
Error Analysis for a Parabolic PDE Model Problem on a Coupled Moving Domain in a Fully Eulerian Framework	8
A Class of Boundary Conditions for Time-Discrete Green--Naghdi Equations with Bathymetry	8
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization	8
Exponential Integrators for Quasilinear Wave-Type Equations	8
A Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates	8
A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning	8
Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance	8
Value-Gradient Based Formulation of Optimal Control Problem and Machine Learning Algorithm	8
Multiple Relaxation Exponential Runge–Kutta Methods for the Nonlinear Schrödinger Equation	7
Computing Semigroups with Error Control	7
On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field	7
Stable Lifting of Polynomial Traces on Triangles	7
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property	7
Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains	7
Duality-Based Error Control for the Signorini Problem	6
Coupling Parareal with Optimized Schwarz Waveform Relaxation for Parabolic Problems	6
A Study of Numerical Pollution of the Decoupled Algorithm for the Convection Model in Superposed Fluid and Porous Layers	6
Bilinear Optimal Control for the Fractional Laplacian: Analysis and Discretization	6
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties	6
Robust Preconditioning and Error Estimates for Optimal Control of the Convection--Diffusion--Reaction Equation with Limited Observation in Isogeometric Analysis	6
Leapfrog Methods for Relativistic Charged-Particle Dynamics	6
Least Squares Approximations in Linear Statistical Inverse Learning Problems	6
Lattice Green’s Functions for High-Order Finite Difference Stencils	6
Error Estimates for Euler Discretization of High-Index Saddle Dynamics	5
${\boldsymbol{H^1}}$ -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation	5
Rational Methods for Abstract, Linear, Nonhomogeneous Problems without Order Reduction	5
A Posteriori Error Estimates for Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes	5
A Uniform Preconditioner for a Newton Algorithm for Total Variation Minimization and Minimum-Surface Problems	5
Achieving High Convergence Rates by Quasi-Monte Carlo and Importance Sampling for Unbounded Integrands	5
Optimal $\boldsymbol{{L^2}}$ Error Estimates of Unconditionally Stable Finite Element Schemes for the Cahn–Hilliard–Navier–Stokes System	5
An Energy-Based Discontinuous Galerkin Method for the Nonlinear Schrödinger Equation with Wave Operator	5
Numerical Attractors for Rough Differential Equations	5
Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps	5
Analysis of a Monte-Carlo Nystrom Method	5
VEM-Nitsche Fully Discrete Polytopal Scheme for Frictionless Contact-Mechanics	5
Pointwise A Posteriori Error Estimates for Discontinuous Galerkin Methods for Singularly Perturbed Reaction-Diffusion Equations	5
The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method	5
Discretization of Total Variation in Optimization with Integrality Constraints	5
Resolution of Singularities by Rational Functions	4
Homogenization of Nondivergence-Form Elliptic Equations with Discontinuous Coefficients and Finite Element Approximation of the Homogenized Problem	4

Implicit and Fully Discrete Approximation of the Supercooled Stefan Problem in the Presence of Blow-Ups	4
Anderson Acceleration for Nonsmooth Fixed Point Problems	4
Accurately Recover Global Quasiperiodic Systems by Finite Points	4
Analytic and Gevrey Class Regularity for Parametric Elliptic Eigenvalue Problems and Applications	4
Optimal Rate of Convergence for Approximations of SPDEs with Nonregular Drift	4
Error Analysis Based on Inverse Modified Differential Equations for Discovery of Dynamics Using Linear Multistep Methods and Deep Learning	4
Quasi-Optimal Error Estimates for the Finite Element Approximation of Stable Harmonic Maps with Nodal Constraints	4
wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws	4
A Monotone, Second Order Accurate Scheme for Curvature Motion	4
Preservation of Quadratic Invariants by Semiexplicit Symplectic Integrators for Nonseparable Hamiltonian Systems	4
A High Order Finite Difference Method for the Elastic Wave Equation in Bounded Domains with Nonconforming Interfaces	4
Finite Element Method for a Nonlinear Perfectly Matched Layer Helmholtz Equation with High Wave Number	4
Localized Implicit Time Stepping for the Wave Equation	4
Harmonic Functions on Finitely Connected Tori	4
Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations	4
Two-Scale Finite Element Approximation of a Homogenized Plate Model	4
Sequential Discretization Schemes for a Class of Stochastic Differential Equations and their Application to Bayesian Filtering	4
$p$ -Robust Equilibrated Flux Reconstruction in $\boldsymbol{H}(\textrm{curl})$ Based on Local Minimizations: Application to a Posteriori Analysis of the Curl-Curl Problem	4
Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions	4
An Exponential Spectral Method Using VP Means for Semilinear Subdiffusion Equations with Rough Data	4
A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains	4
Radial Complex Scaling for Anisotropic Scalar Resonance Problems	4
Numerical Analysis of a Discontinuous Galerkin Method for the Borrvall--Petersson Topology Optimization Problem	4
Full Discretization of Cauchy's Problem by Lavrentiev--Finite Element Method	4
Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data	4
On the Computation of Gaussian Quadrature Rules for Chebyshev Sets of Linearly Independent Functions	4

High Order Biorthogonal Functions in \({H}\)(curl)	10
\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension	10
A Local Discontinuous Galerkin Approximation for the \(\boldsymbol{{p}}\) -Navier–Stokes System, Part II: Convergence Rates for the Velocity	9
Sparse Monte Carlo Method for Nonlocal Diffusion Problems	9
Efficient Approximation of SDEs Driven by Countably Dimensional Wiener Process and Poisson Random Measure	9
Local Convergence of the FEM for the Integral Fractional Laplacian	9
On the Finite Element Approximation of a Semicoercive Stokes Variational Inequality Arising in Glaciology	9
Nonlinear Eigenvalue Methods for Linear Pointwise Stability of Nonlinear Waves	8
Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model	8
Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons	8
Error Analysis for a Parabolic PDE Model Problem on a Coupled Moving Domain in a Fully Eulerian Framework	8
A Class of Boundary Conditions for Time-Discrete Green--Naghdi Equations with Bathymetry	8
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization	8
Exponential Integrators for Quasilinear Wave-Type Equations	8
A Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates	8
A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning	8
Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance	8
Value-Gradient Based Formulation of Optimal Control Problem and Machine Learning Algorithm	8
Multiple Relaxation Exponential Runge–Kutta Methods for the Nonlinear Schrödinger Equation	7
Computing Semigroups with Error Control	7
On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field	7
Stable Lifting of Polynomial Traces on Triangles	7
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property	7
Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains	7
Duality-Based Error Control for the Signorini Problem	6
Coupling Parareal with Optimized Schwarz Waveform Relaxation for Parabolic Problems	6
A Study of Numerical Pollution of the Decoupled Algorithm for the Convection Model in Superposed Fluid and Porous Layers	6
Bilinear Optimal Control for the Fractional Laplacian: Analysis and Discretization	6
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties	6
Robust Preconditioning and Error Estimates for Optimal Control of the Convection--Diffusion--Reaction Equation with Limited Observation in Isogeometric Analysis	6
Leapfrog Methods for Relativistic Charged-Particle Dynamics	6
Least Squares Approximations in Linear Statistical Inverse Learning Problems	6
Lattice Green’s Functions for High-Order Finite Difference Stencils	6
Error Estimates for Euler Discretization of High-Index Saddle Dynamics	5
\({\boldsymbol{H^1}}\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation	5
Rational Methods for Abstract, Linear, Nonhomogeneous Problems without Order Reduction	5
A Posteriori Error Estimates for Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes	5
A Uniform Preconditioner for a Newton Algorithm for Total Variation Minimization and Minimum-Surface Problems	5
Achieving High Convergence Rates by Quasi-Monte Carlo and Importance Sampling for Unbounded Integrands	5
Optimal \(\boldsymbol{{L^2}}\) Error Estimates of Unconditionally Stable Finite Element Schemes for the Cahn–Hilliard–Navier–Stokes System	5
An Energy-Based Discontinuous Galerkin Method for the Nonlinear Schrödinger Equation with Wave Operator	5
Numerical Attractors for Rough Differential Equations	5
Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps	5
Analysis of a Monte-Carlo Nystrom Method	5
VEM-Nitsche Fully Discrete Polytopal Scheme for Frictionless Contact-Mechanics	5
Pointwise A Posteriori Error Estimates for Discontinuous Galerkin Methods for Singularly Perturbed Reaction-Diffusion Equations	5
The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method	5
Discretization of Total Variation in Optimization with Integrality Constraints	5
Resolution of Singularities by Rational Functions	4
Homogenization of Nondivergence-Form Elliptic Equations with Discontinuous Coefficients and Finite Element Approximation of the Homogenized Problem	4