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 2020-11-01 to 2024-11-01.)

Article	Citations
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs	152
An adaptive BDF2 implicit time-stepping method for the phase field crystal model	52
Estimates on the generalization error of physics-informed neural networks for approximating PDEs	44
Error estimates for physics-informed neural networks approximating the Navier–Stokes equations	30
Anderson acceleration for contractive and noncontractive operators	30
Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework	25
Automatic rational approximation and linearization of nonlinear eigenvalue problems	23
Simulation of McKean–Vlasov SDEs with super-linear growth	22
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem	18
A strong order 3/4 method for SDEs with discontinuous drift coefficient	18
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains	18
The time-fractional Cahn–Hilliard equation: analysis and approximation	17
Numerical methods for stochastic Volterra integral equations with weakly singular kernels	16
Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation	16
Error estimate of a decoupled numerical scheme for the Cahn–Hilliard–Stokes–Darcy system	15
Uniform error estimates for artificial neural network approximations for heat equations	15
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H	15
Log orthogonal functions: approximation properties and applications	14
Optimally convergent mixed finite element methods for the stochastic Stokes equations	13
Stabilization parameter analysis of a second-order linear numerical scheme for the nonlocal Cahn–Hilliard equation	13
Strong convergence of Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations under local Lipschitz conditions of state variables	13
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions	13
Space–time discontinuous Galerkin approximation of acoustic waves with point singularities	13
An Lpspaces-based formulation yielding a new fully mixed finite element method for the coupled Darcy and heat equations	12
Optimal convergence of a second-order low-regularity integrator for the KdV equation	12

A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains	12
From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation	11
Exact and inexact Douglas–Rachford splitting methods for solving large-scale sparse absolute value equations	11
Solving time-fractional differential equations via rational approximation	10
Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise	10
Anisotropic a posteriori error estimate for the virtual element method	9
An HDG method for dissimilar meshes	9
Error bounds for overdetermined and underdetermined generalized centred simplex gradients	9
A C1-virtual element method of high order for the Brinkman equations in stream function formulation with pressure recovery	9
Numerical analysis of the LDG method for large deformations of prestrained plates	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
Uniform convergence rates for Lipschitz learning on graphs	8
Homogeneous multigrid for HDG	8
A posteriori error estimates with boundary correction for a cut finite element method	8
Semirobust analysis of an H(div)-conforming DG method with semi-implicit time-marching for the evolutionary incompressible Navier–Stokes equations	8
Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients	8
Interpolation and stability properties of low-order face and edge virtual element spaces	8
First order least-squares formulations for eigenvalue problems	8
The parabolic p-Laplacian with fractional differentiability	8
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations	7
Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure	7
A spectral-in-time Newton–Krylov method for nonlinear PDE-constrained optimization	7
Space–time discretization for nonlinear parabolic systems withp-structure	7
Optimal rates of convergence and error localization of Gegenbauer projections	7
Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions	7
Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision	7
Derivative-free high-order uniformly accurate schemes for highly oscillatory systems	7
Robust error bounds for the Navier–Stokes equations using implicit-explicit second-order BDF method with variable steps	7
Error analysis for space discretizations of quasilinear wave-type equations	7
Consistency analysis of the Grünwald–Letnikov approximation in a bounded domain	6
An unconditionally energy stable finite element scheme for a nonlinear fluid–fluid interaction model	6
Strong error estimates for a space-time discretization of the linear-quadratic control problem with the stochastic heat equation with linear noise	6
Mixed precision low-rank approximations and their application to block low-rank LU factorization	6
A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem	6
Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions	6
Numerical analysis for nematic electrolytes	6
Tangential errors of tensor surface finite elements	6
A low-order divergence-free H(div)-conforming finite element method for Stokes flows	6
Approximation of fractional harmonic maps	6
Variational convergence of discrete elasticae	6
The numerical unified transform method for initial-boundary value problems on the half-line	6
Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes	6
Fast mass lumped multiscale wave propagation modelling	6
Solving block low-rank linear systems by LU factorization is numerically stable	6
An adaptive edge finite element DtN method for Maxwell’s equations in biperiodic structures	6
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: efficient algorithms and numerical results	6
Virtual element method for the Navier–Stokes equation coupled with the heat equation	6
The Scharfetter–Gummel scheme for aggregation–diffusion equations	6
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes	5
Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces	5

L 2 norm error estimates of BDF methods up to fifth-order for the phase field crystal model	5
Adaptive sampling strategies for risk-averse stochastic optimization with constraints	5
Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints	5
Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems	5
Shanks and Anderson-type acceleration techniques for systems of nonlinear equations	5
Maximal regularity of multistep fully discrete finite element methods for parabolic equations	5
Eigenvalue bounds for double saddle-point systems	5
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: regularity and error analysis	5
Construction and application of provable positive and exact cubature formulas	5
A second-order accurate numerical scheme for a time-fractional Fokker–Planck equation	5
Fast and accurate approximations to fractional powers of operators	5
Applications of a space-time FOSLS formulation for parabolic PDEs	5
A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian submanifolds in Euclidean space	5
A convergent finite element algorithm for generalized mean curvature flows of closed surfaces	4
A consistent quasi–second-order staggered scheme for the two-dimensional shallow water equations	4
A new second-order low-regularity integrator for the cubic nonlinear Schrödinger equation	4
Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients	4
Augmented saddle-point formulation of the steady-state Stefan–Maxwell diffusion problem	4
Spectral Galerkin method for solving Helmholtz boundary integral equations on smooth screens	4
Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data	4
Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions	4
A general collocation analysis for weakly singular Volterra integral equations with variable exponent	4
A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour	4
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM	4
A proximal bundle algorithm for nonsmooth optimization on Riemannian manifolds	4
Fast global spectral methods for three-dimensional partial differential equations	4
On symmetric positive definite preconditioners for multiple saddle-point systems	4
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator	4
On the convergence of augmented Lagrangian strategies for nonlinear programming	4
Continuous Galerkin schemes for semiexplicit differential-algebraic equations	4
An HDG method for the Steklov eigenvalue problem	4
A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems	4
Convergence analysis of subdivision processes on the sphere	4
Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations	4
Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature	4
Robust multigrid methods for nearly incompressible elasticity using macro elements	4
A two-stage approximation strategy for piecewise smooth functions in two and three dimensions	4
A family of fast fixed point iterations for M/G/1-type Markov chains	4
Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin-walled structure: stability and convergence analysis	4
Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves	4
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation	4