IMA Journal of Numerical Analysis

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
Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework	23
Estimates on the generalization error of physics-informed neural networks for approximating PDEs	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
Numerical methods for stochastic Volterra integral equations with weakly singular kernels	13
The time-fractional Cahn–Hilliard equation: analysis and approximation	13

Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H	13
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
Orthogonal structure on a quadratic curve	12
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
hp-FEM for the fractional heat equation	11
Variational integrators for stochastic dissipative Hamiltonian systems	11
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
A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees	10
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
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions	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
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
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
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
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
Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints	5
Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces	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
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
Stabilization parameter analysis of a second-order linear numerical scheme for the nonlocal Cahn–Hilliard equation	5
Variational convergence of discrete elasticae	5
Exact and inexact Douglas–Rachford splitting methods for solving large-scale sparse absolute value equations	5
Contour integrals of analytic functions given on a grid in the complex plane	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
The Scharfetter–Gummel scheme for aggregation–diffusion equations	5
On critical points of quadratic low-rank matrix optimization problems	4
Shanks and Anderson-type acceleration techniques for systems of nonlinear equations	4
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
Convergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernel	3
Spectral Galerkin method for solving Helmholtz boundary integral equations on smooth screens	3
A family of fast fixed point iterations for M/G/1-type Markov chains	3
Fast and accurate approximations to fractional powers of operators	3
Fast mass lumped multiscale wave propagation modelling	3
Galerkin approximation of linear problems in Banach and Hilbert spaces	3
A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems	3
A mixed-primal finite element method for the coupling of Brinkman–Darcy flow and nonlinear transport	3
Quasi-reliable estimates of effective sample size	3
Fast global spectral methods for three-dimensional partial differential equations	3
Augmented saddle-point formulation of the steady-state Stefan–Maxwell diffusion problem	3
Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems	3
Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin-walled structure: stability and convergence analysis	3
Localized inverse factorization	3
A second-order discretization for degenerate systems of stochastic differential equations	3
Error analysis for full discretizations of quasilinear wave-type equations with two variants of the implicit midpoint rule	3
Eigenvalue bounds for double saddle-point systems	3
A locking-free P0 finite element method for linear elasticity equations on polytopal partitions	3
Convergence analysis of subdivision processes on the sphere	3
A proximal bundle algorithm for nonsmooth optimization on Riemannian manifolds	3
Robust multigrid methods for nearly incompressible elasticity using macro elements	3
Continuous Galerkin schemes for semiexplicit differential-algebraic equations	3
Fast wavelet decomposition of linear operators through product-convolution expansions	3
An HDG method for the Steklov eigenvalue problem	3
An algorithm for calculating Hermite-based finite difference weights	3
Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions	3
Randomized sketch descent methods for non-separable linearly constrained optimization	3
Post-processing of the planewave approximation of Schrödinger equations. Part I: linear operators	3
A new second-order low-regularity integrator for the cubic nonlinear Schrödinger equation	3
Analysis of backward Euler projection FEM for the Landau–Lifshitz equation	3
Robusta posteriorierror estimation for mixed finite element approximation of linear poroelasticity	3
Multilevel representations of isotropic Gaussian random fields on the sphere	2
A sharp error estimate of piecewise polynomial collocation for nonlocal problems with weakly singular kernels	2

Regularizing linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements	2
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator	2
Numerical analysis of two-dimensional Navier–Stokes equations with additive stochastic forcing	2
Infinite-order accuracy limit of finite difference formulas in the complex plane	2
Numerical homogenization for nonlinear strongly monotone problems	2
Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates	2
Two-point Landweber-type method with convex penalty terms for nonsmooth nonlinear inverse problems	2
On a time-discrete convolution—space collocation BEM for the numerical solution of two-dimensional wave propagation problems in unbounded domains	2
Variational analysis of the discontinuous Galerkin time-stepping method for parabolic equations	2
A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian submanifolds in Euclidean space	2
Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term	2
On symmetric positive definite preconditioners for multiple saddle-point systems	2
Nonselfadjoint impedance in Generalized Optimized Schwarz Methods	2
Projection-free nonconvex stochastic optimization on Riemannian manifolds	2
Finite-volume approximation of the invariant measure of a viscous stochastic scalar conservation law	2
Wavelet–Fourier CORSING techniques for multidimensional advection–diffusion–reaction equations	2
A convergent finite element scheme for a fourth-order liquid crystal model	2
Numerical analysis of a wave equation for lossy media obeying a frequency power law	2
Approximation of SPDE covariance operators by finite elements: a semigroup approach	2
A second-order accurate numerical scheme for a time-fractional Fokker–Planck equation	2
On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field	2
The dual inverse scaling and squaring algorithm for the matrix logarithm	2
A posteriori error estimation and space-time adaptivity for a linear stochastic PDE with additive noise	2
A low-order divergence-free H(div)-conforming finite element method for Stokes flows	2
Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions	2
L2 norm error estimates of BDF methods up to fifth-order for the phase field crystal model	2
Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes	2
A convergent finite element algorithm for generalized mean curvature flows of closed surfaces	2
A variational approach to the sum splitting scheme	2
Convergence, error analysis and longtime behavior of the scalar auxiliary variable method for the nonlinear Schrödinger equation	2
hp-FEM for reaction–diffusion equations. II: robust exponential convergence for multiple length scales in corner domains	2
Virtual element method for the Navier–Stokes equation coupled with the heat equation	2
Linear schemes with several degrees of freedom for the transport equation and the long-time simulation accuracy	2
Variable order, directional ℋ2-matrices for Helmholtz problems with complex frequency	2
Wavelet-based approximations of pointwise bound constraints in Lebesgue and Sobolev spaces	2
Convergence of a multidimensional Glimm-like scheme for the transport of fronts	2
Scaling of radial basis functions	2
Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton-type methods via range invariance	2
On the rate of convergence of a numerical scheme for Fractional conservation laws with noise	2
A high-frequency boundary element method for scattering by a class of multiple obstacles	2
Weak and strong error analysis of recursive quantization: a general approach with an application to jump diffusions	2
Optimal numerical integration and approximation of functions on ℝd equipped with Gaussian measure	2
A discontinuous Galerkin coupling for nonlinear elasto-acoustics	2
Local multigrid solvers for adaptive isogeometric analysis in hierarchical spline spaces	2
Stability analysis of general multistep methods for Markovian backward stochastic differential equations	2
Applications of a space-time FOSLS formulation for parabolic PDEs	2
A two-stage approximation strategy for piecewise smooth functions in two and three dimensions	2
Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations	2
A high-order fully discrete scheme for the Korteweg–de Vries equation with a time-stepping procedure of Runge–Kutta-composition type	2
Structure-preserving discretizations of gradient flows for axisymmetric two-phase biomembranes	2
Error estimates for a linear folding model	2
Spurious solutions for high-order curl problems	1
On the minimum value of the condition number of polynomials	1
Application of the Crank–Nicolson time integrator to viscoelastic wave equations with boundary feedback damping	1
A modified limited memory steepest descent method motivated by an inexact super-linear convergence rate analysis	1
Divergence-conforming methods for transient double-diffusive flows: a priori and a posteriori error analysis	1
On QZ steps with perfect shifts and computing the index of a differential-algebraic equation	1
A convergent SAV scheme for Cahn–Hilliard equations with dynamic boundary conditions	1
Numerical solution of anH(curl)-elliptic hemivariational inequality	1
A constructive low-regularity integrator for the one-dimensional cubic nonlinear Schrödinger equation under Neumann boundary condition	1
Convergence of preconditioned Hamiltonian Monte Carlo on Hilbert spaces	1
Maximum norm error bounds for the full discretization of nonautonomous wave equations	1
A nodally bound-preserving finite element method	1
An a priori error analysis of adjoint-based super-convergent Galerkin approximations of linear functionals	1
A sub-sampled tensor method for nonconvex optimization	1
Finite element analysis for a diffusion equation on a harmonically evolving domain	1
A convergent FV–FE scheme for the stationary compressible Navier–Stokes equations	1
Error estimates for the numerical approximation of optimal control problems with nonsmooth pointwise-integral control constraints	1
Error bound and exact penalty method for optimization problems with nonnegative orthogonal constraint	1
A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations	1
A locking-free staggered DG method for the Biot system of poroelasticity on general polygonal meshes	1
Modeling Hessian-vector products in nonlinear optimization: new Hessian-free methods	1
A novel spectral method for the semiclassical Schrödinger equation based on the Gaussian wave-packet transform	1
Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients	1
Pressure robust SUPG-stabilized finite elements for the unsteady Navier–Stokes equation	1
Global and explicit approximation of piecewise-smooth two-dimensional functions from cell-average data	1
Padé-parametric FEM approximation for fractional powers of elliptic operators on manifolds	1
Exponential convergence of mixed hp-DGFEM for the incompressible Navier–Stokes equations in ℝ2	1
Low regularity exponential-type integrators for the “good” Boussinesq equation	1
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems	1
Optimal convergence of arbitrary Lagrangian–Eulerian iso-parametric finite element methods for parabolic equations in an evolving domain	1
Adaptive quarkonial domain decomposition methods for elliptic partial differential equations	1
Cubature rules from Hall–Littlewood polynomials	1
The Kirchhoff plate equation on surfaces: the surface Hellan–Herrmann–Johnson method	1
A symmetric low-regularity integrator for the nonlinear Schrödinger equation	1
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs	1
Solvability of discrete Helmholtz equations	1
Adaptive regularization minimization algorithms with nonsmooth norms	1
Efficient implementation of the exact artificial boundary condition for the exterior problem of the Stokes system in three dimensions	1
Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements	1
Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density	1
Transfer of conservative discrete differential operators between staggered grids: construction and duality relations	1
Multiresolution analysis for stochastic hyperbolic conservation laws	1
Recursive moment computation in Filon methods and application to high-frequency wave scattering in two dimensions	1
Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems	1