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 2020-05-01 to 2024-05-01.)

Article	Citations
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs	123
Blow-up of error estimates in time-fractional initial-boundary value problems	64
An adaptive BDF2 implicit time-stepping method for the phase field crystal model	42
Accurately computing the log-sum-exp and softmax functions	35
Estimates on the generalization error of physics-informed neural networks for approximating PDEs	27
Anderson acceleration for contractive and noncontractive operators	26
Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework	23
Automatic rational approximation and linearization of nonlinear eigenvalue problems	21
Simulation of McKean–Vlasov SDEs with super-linear growth	20
The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem	18
Energy-preserving methods for nonlinear Schrödinger equations	18
A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model	18
Error estimates for physics-informed neural networks approximating the Navier–Stokes equations	17
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem	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	16
The time-fractional Cahn–Hilliard equation: analysis and approximation	15
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains	15
Uniform error estimates for artificial neural network approximations for heat equations	14
Numerical methods for stochastic Volterra integral equations with weakly singular kernels	14
Strong error analysis for stochastic gradient descent optimization algorithms	14
An energy-stable parametric finite element method for simulating solid-state dewetting	14
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H	13
An unfitted hybrid high-order method for the Stokes interface problem	12
Optimal convergence of a second-order low-regularity integrator for the KdV equation	12

Space–time discontinuous Galerkin approximation of acoustic waves with point singularities	12
A strong order 3/4 method for SDEs with discontinuous drift coefficient	12
Variational integrators for stochastic dissipative Hamiltonian systems	12
A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains	11
Log orthogonal functions: approximation properties and applications	11
On the complexity of an augmented Lagrangian method for nonconvex optimization	11
Error estimate of a decoupled numerical scheme for the Cahn–Hilliard–Stokes–Darcy system	10
Optimally convergent mixed finite element methods for the stochastic Stokes equations	10
Strong convergence of Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations under local Lipschitz conditions of state variables	10
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions	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
An HDG method for dissimilar meshes	9
Solving time-fractional differential equations via rational approximation	9
An Lpspaces-based formulation yielding a new fully mixed finite element method for the coupled Darcy and heat equations	8
Anisotropic a posteriori error estimate for the virtual element method	8
A C1-virtual element method of high order for the Brinkman equations in stream function formulation with pressure recovery	8
From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation	8
A finite element error analysis for axisymmetric mean curvature flow	8
Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients	8
Error bounds for overdetermined and underdetermined generalized centred simplex gradients	8
Symmetric pressure stabilization for equal-order finite element approximations to the time-dependent Navier–Stokes equations	8
Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt method	7
Stirling numbers and Gregory coefficients for the factorization of Hermite subdivision operators	7
Quantitative stability and error estimates for optimal transport plans	7
Trace finite element methods for surface vector-Laplace equations	7
Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure	7
Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise	7
A posteriori error estimates with boundary correction for a cut finite element method	7
Trace operators of the bi-Laplacian and applications	7
Numerical analysis of the LDG method for large deformations of prestrained plates	7
Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions	7
Multivariate approximation of functions on irregular domains by weighted least-squares methods	7
Interpolation and stability properties of low-order face and edge virtual element spaces	7
Space–time discretization for nonlinear parabolic systems withp-structure	7
Robust error bounds for the Navier–Stokes equations using implicit-explicit second-order BDF method with variable steps	7
A spectral-in-time Newton–Krylov method for nonlinear PDE-constrained optimization	7
The numerical unified transform method for initial-boundary value problems on the half-line	6
Homogeneous multigrid for HDG	6
Consistency analysis of the Grünwald–Letnikov approximation in a bounded domain	6
Contour integrals of analytic functions given on a grid in the complex plane	6
Analysis of an interior penalty DG method for the quad-curl problem	6
Stabilization parameter analysis of a second-order linear numerical scheme for the nonlocal Cahn–Hilliard equation	6
Numerical analysis for nematic electrolytes	6
Error analysis for space discretizations of quasilinear wave-type equations	6
The parabolic p-Laplacian with fractional differentiability	6
Solving block low-rank linear systems by LU factorization is numerically stable	6
Derivative-free high-order uniformly accurate schemes for highly oscillatory systems	6
Hermite interpolation on the unit sphere and limits of Lagrange projectors	6
On the convergence of a finite volume method for the Navier–Stokes–Fourier system	6
Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision	6

Strong error estimates for a space-time discretization of the linear-quadratic control problem with the stochastic heat equation with linear noise	6
Residual-baseda posteriorierror estimates of mixed methods for a three-field Biot’s consolidation model	6
Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation	6
Approximation of fractional harmonic maps	5
First order least-squares formulations for eigenvalue problems	5
Uniform convergence rates for Lipschitz learning on graphs	5
Optimal rates of convergence and error localization of Gegenbauer projections	5
Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions	5
Optimal error estimates and recovery technique of a mixed finite element method for nonlinear thermistor equations	5
Semirobust analysis of an H(div)-conforming DG method with semi-implicit time-marching for the evolutionary incompressible Navier–Stokes equations	5
Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier–Stokes equations	5
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations	5
Variational convergence of discrete elasticae	5
The Scharfetter–Gummel scheme for aggregation–diffusion equations	5
Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces	5
A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem	5
Eigenvalue bounds for double saddle-point systems	5
Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms	5
Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions	5
Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints	5
Exact and inexact Douglas–Rachford splitting methods for solving large-scale sparse absolute value equations	5
An adaptive edge finite element DtN method for Maxwell’s equations in biperiodic structures	4
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM	4
Augmented saddle-point formulation of the steady-state Stefan–Maxwell diffusion problem	4
On the convergence of augmented Lagrangian strategies for nonlinear programming	4
Shanks and Anderson-type acceleration techniques for systems of nonlinear equations	4
Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals	4
An HDG method for the Steklov eigenvalue problem	4
Post-processing of the plane-wave approximation of Schrödinger equations. Part II: Kohn–Sham models	4
Applications of a space-time FOSLS formulation for parabolic PDEs	4
Mixed precision low-rank approximations and their application to block low-rank LU factorization	4
A proximal bundle algorithm for nonsmooth optimization on Riemannian manifolds	4
A family of fast fixed point iterations for M/G/1-type Markov chains	4
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes	4
Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data	4
Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation	4
Randomized sketch descent methods for non-separable linearly constrained optimization	4
Maximal regularity of multistep fully discrete finite element methods for parabolic equations	4
A consistent quasi–second-order staggered scheme for the two-dimensional shallow water equations	4
Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature	4
A second-order accurate numerical scheme for a time-fractional Fokker–Planck equation	4
Construction and application of provable positive and exact cubature formulas	4
Tangential errors of tensor surface finite elements	4
Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions	4
Fast and accurate approximations to fractional powers of operators	4
Adaptive sampling strategies for risk-averse stochastic optimization with constraints	4