OOIR: Observatory of International Research

Papers

(The TQCC of IMA Journal of 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 2020-03-01 to 2024-03-01.)

Article	Citations
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs	103
Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions	60
Blow-up of error estimates in time-fractional initial-boundary value problems	56
An adaptive BDF2 implicit time-stepping method for the phase field crystal model	38
Accurately computing the log-sum-exp and softmax functions	32
Anderson acceleration for contractive and noncontractive operators	25
Estimates on the generalization error of physics-informed neural networks for approximating PDEs	23
Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework	23
Automatic rational approximation and linearization of nonlinear eigenvalue problems	19
A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model	18
Simulation of McKean–Vlasov SDEs with super-linear growth	17
Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization	17
The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem	17
Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem	17
Energy-preserving methods for nonlinear Schrödinger equations	16
Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation	16
A Banach space mixed formulation for the unsteady Brinkman–Forchheimer equations	15
Uniform error estimates for artificial neural network approximations for heat equations	14
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem	14
Error estimates for physics-informed neural networks approximating the Navier–Stokes equations	14
On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators	14
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains	14
Strong error analysis for stochastic gradient descent optimization algorithms	14
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H	13
Numerical methods for stochastic Volterra integral equations with weakly singular kernels	13

The time-fractional Cahn–Hilliard equation: analysis and approximation	13
Orthogonal structure on a quadratic curve	12
An energy-stable parametric finite element method for simulating solid-state dewetting	12
Space–time discontinuous Galerkin approximation of acoustic waves with point singularities	12
hp-FEM for the fractional heat equation	11
Variational integrators for stochastic dissipative Hamiltonian systems	11
A strong order 3/4 method for SDEs with discontinuous drift coefficient	11
A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains	11
Optimal convergence of a second-order low-regularity integrator for the KdV equation	11
Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity	11
A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees	10
An unfitted hybrid high-order method for the Stokes interface problem	10
Error estimate of a decoupled numerical scheme for the Cahn–Hilliard–Stokes–Darcy system	10
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions	9
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions	9
An HDG method for dissimilar meshes	9
Log orthogonal functions: approximation properties and applications	9
On the complexity of an augmented Lagrangian method for nonconvex optimization	9
Consistency, convergence and error estimates for a mixed finite element–finite volume scheme to compressible Navier–Stokes equations with general inflow/outflow boundary data	9
Error bounds for overdetermined and underdetermined generalized centred simplex gradients	8
A finite element error analysis for axisymmetric mean curvature flow	8
Optimally convergent mixed finite element methods for the stochastic Stokes equations	8
Symmetric pressure stabilization for equal-order finite element approximations to the time-dependent Navier–Stokes equations	8
Stirling numbers and Gregory coefficients for the factorization of Hermite subdivision operators	7
A posteriori error estimates with boundary correction for a cut finite element method	7
Space–time discretization for nonlinear parabolic systems withp-structure	7
A C1-virtual element method of high order for the Brinkman equations in stream function formulation with pressure recovery	7
An Lpspaces-based formulation yielding a new fully mixed finite element method for the coupled Darcy and heat equations	7
Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt method	7
Anisotropic a posteriori error estimate for the virtual element method	7
Trace finite element methods for surface vector-Laplace equations	7
Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients	7
Multivariate approximation of functions on irregular domains by weighted least-squares methods	7
From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation	7
Quantitative stability and error estimates for optimal transport plans	7
Trace operators of the bi-Laplacian and applications	7
Robust error bounds for the Navier–Stokes equations using implicit-explicit second-order BDF method with variable steps	6
Numerical analysis for nematic electrolytes	6
Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions	6
A spectral-in-time Newton–Krylov method for nonlinear PDE-constrained optimization	6
Consistency analysis of the Grünwald–Letnikov approximation in a bounded domain	6
Strong error estimates for a space-time discretization of the linear-quadratic control problem with the stochastic heat equation with linear noise	6
Numerical analysis of the LDG method for large deformations of prestrained plates	6
Analysis of an interior penalty DG method for the quad-curl problem	6
Hermite interpolation on the unit sphere and limits of Lagrange projectors	6
Finite element error analysis of wave equations with dynamic boundary conditions:L2 estimates	6
Homogeneous multigrid for HDG	6
Error analysis for space discretizations of quasilinear wave-type equations	6
The parabolic p-Laplacian with fractional differentiability	6
Strong convergence of Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations under local Lipschitz conditions of state variables	6

Derivative-free high-order uniformly accurate schemes for highly oscillatory systems	6
Solving time-fractional differential equations via rational approximation	6
The numerical unified transform method for initial-boundary value problems on the half-line	6
On the convergence of a finite volume method for the Navier–Stokes–Fourier system	6
Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure	6
Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision	6
Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise	6
Solving block low-rank linear systems by LU factorization is numerically stable	6
Residual-baseda posteriorierror estimates of mixed methods for a three-field Biot’s consolidation model	6
Interpolation and stability properties of low-order face and edge virtual element spaces	6
Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces	5
The Scharfetter–Gummel scheme for aggregation–diffusion equations	5
Uniform convergence rates for Lipschitz learning on graphs	5
Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions	5
Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms	5
Optimal error estimates and recovery technique of a mixed finite element method for nonlinear thermistor equations	5
Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions	5
Semirobust analysis of an H(div)-conforming DG method with semi-implicit time-marching for the evolutionary incompressible Navier–Stokes equations	5
Stabilization parameter analysis of a second-order linear numerical scheme for the nonlocal Cahn–Hilliard equation	5
Variational convergence of discrete elasticae	5
Contour integrals of analytic functions given on a grid in the complex plane	5
Exact and inexact Douglas–Rachford splitting methods for solving large-scale sparse absolute value equations	5
Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation	5
Optimal rates of convergence and error localization of Gegenbauer projections	5
Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints	5
On the convergence of augmented Lagrangian strategies for nonlinear programming	4
Post-processing of the plane-wave approximation of Schrödinger equations. Part II: Kohn–Sham models	4
An adaptive edge finite element DtN method for Maxwell’s equations in biperiodic structures	4
A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem	4
Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier–Stokes equations	4
Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data	4
Construction and application of provable positive and exact cubature formulas	4
Approximation of fractional harmonic maps	4
Adaptive sampling strategies for risk-averse stochastic optimization with constraints	4
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations	4
First order least-squares formulations for eigenvalue problems	4
A consistent quasi–second-order staggered scheme for the two-dimensional shallow water equations	4
Tangential errors of tensor surface finite elements	4
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes	4
Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals	4
Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation	4
Maximal regularity of multistep fully discrete finite element methods for parabolic equations	4
Mixed precision low-rank approximations and their application to block low-rank LU factorization	4
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM	4
Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature	4
On critical points of quadratic low-rank matrix optimization problems	4
Shanks and Anderson-type acceleration techniques for systems of nonlinear equations	4