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	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
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H	15
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
Log orthogonal functions: approximation properties and applications	14
Space–time discontinuous Galerkin approximation of acoustic waves with point singularities	13
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
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
The parabolic p-Laplacian with fractional differentiability	8
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
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
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
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 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 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
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
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
On the rate of convergence of a numerical scheme for Fractional conservation laws with noise	3
Finite-volume approximation of the invariant measure of a viscous stochastic scalar conservation law	3
Pressure robust SUPG-stabilized finite elements for the unsteady Navier–Stokes equation	3
Modeling Hessian-vector products in nonlinear optimization: new Hessian-free methods	3
Fully discrete best-approximation-type estimates inL∞ (I;L2(Ω)d) for finite element discretizations of the transient Stokes equations	3
Error analysis for full discretizations of quasilinear wave-type equations with two variants of the implicit midpoint rule	3
Darcy’s problem coupled with the heat equation under singular forcing: analysis and discretization	3
A locking-free P0 finite element method for linear elasticity equations on polytopal partitions	3
Analysis of backward Euler projection FEM for the Landau–Lifshitz equation	3
Variable order, directional ℋ2-matrices for Helmholtz problems with complex frequency	3
Convergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernel	3
Numerical analysis of two-dimensional Navier–Stokes equations with additive stochastic forcing	3
Error estimates for finite differences approximations of the total variation	3
Infinite-order accuracy limit of finite difference formulas in the complex plane	3
A constructive low-regularity integrator for the one-dimensional cubic nonlinear Schrödinger equation under Neumann boundary condition	3
Numerical solution of anH(curl)-elliptic hemivariational inequality	3
Multilevel representations of isotropic Gaussian random fields on the sphere	3
Two-point Landweber-type method with convex penalty terms for nonsmooth nonlinear inverse problems	3
Low regularity exponential-type integrators for the “good” Boussinesq equation	2
Approximation of SPDE covariance operators by finite elements: a semigroup approach	2
A discontinuous Galerkin coupling for nonlinear elasto-acoustics	2
A C0 finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain	2
Recursive moment computation in Filon methods and application to high-frequency wave scattering in two dimensions	2
Numerical homogenization for nonlinear strongly monotone problems	2
Multiresolution analysis for stochastic hyperbolic conservation laws	2
A locking-free staggered DG method for the Biot system of poroelasticity on general polygonal meshes	2
A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs	2
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems	2
Random points are optimal for the approximation of Sobolev functions	2
On the minimum value of the condition number of polynomials	2
Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure	2
Projection-free nonconvex stochastic optimization on Riemannian manifolds	2
Regularizing linear inverse problems under unknown non-Gaussian white noise allowing repeated measurements	2
A variational approach to the sum splitting scheme	2
A posteriori error estimation and space-time adaptivity for a linear stochastic PDE with additive noise	2
Multiple projection Markov chain Monte Carlo algorithms on submanifolds	2
Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross–Pitaevskii equation with rotation	2
Numerical analysis of a wave equation for lossy media obeying a frequency power law	2
Padé-parametric FEM approximation for fractional powers of elliptic operators on manifolds	2

Inexact Newton-CG algorithms with complexity guarantees	2
Stability analysis of general multistep methods for Markovian backward stochastic differential equations	2
Milstein schemes and antithetic multilevel Monte Carlo sampling for delay McKean–Vlasov equations and interacting particle systems	2
A symmetric low-regularity integrator for the nonlinear Schrödinger equation	2
Simulation of constrained elastic curves and application to a conical sheet indentation problem	2
Multilevel quasi-interpolation	2
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs	2
Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton-type methods via range invariance	2
Error estimates for a linear folding model	2
On the convergence and mesh-independent property of the Barzilai–Borwein method for PDE-constrained optimization	2
A high-order fully discrete scheme for the Korteweg–de Vries equation with a time-stepping procedure of Runge–Kutta-composition type	2
Error estimates for a splitting integrator for abstract semilinear boundary coupled systems	2
hp-FEM for reaction–diffusion equations. II: robust exponential convergence for multiple length scales in corner domains	2
Ana posteriorierror estimator for isogeometric analysis on trimmed geometries	2
Uniform block-diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes equations and the linear elasticity equations	2
The MHM Method for Linear Elasticity on Polytopal Meshes	2
Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements	2
Convergence of a multidimensional Glimm-like scheme for the transport of fronts	2
On a time-discrete convolution—space collocation BEM for the numerical solution of two-dimensional wave propagation problems in unbounded domains	2
Limits and consistency of nonlocal and graph approximations to the Eikonal equation	2
Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions	2
The dual inverse scaling and squaring algorithm for the matrix logarithm	2
Optimal numerical integration and approximation of functions on ℝd equipped with Gaussian measure	2
A convergent SAV scheme for Cahn–Hilliard equations with dynamic boundary conditions	2
Solvability of discrete Helmholtz equations	2
Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density	2
Continuous interior penalty stabilization for divergence-free finite element methods	2
Adaptive regularization minimization algorithms with nonsmooth norms	2
Local multigrid solvers for adaptive isogeometric analysis in hierarchical spline spaces	2
A nodally bound-preserving finite element method	2
Convergence, error analysis and longtime behavior of the scalar auxiliary variable method for the nonlinear Schrödinger equation	2
Linear schemes with several degrees of freedom for the transport equation and the long-time simulation accuracy	2
Nonselfadjoint impedance in Generalized Optimized Schwarz Methods	2
An augmented fully mixed formulation for the quasistatic Navier–Stokes–Biot model	2
Scaling of radial basis functions	2
Regularity analysis for SEEs with multiplicative fBms and strong convergence for a fully discrete scheme	1
Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function	1
An exponentially convergent discretization for space–time fractional parabolic equations using hp-FEM	1
Finite element analysis for a diffusion equation on a harmonically evolving domain	1
On the approximation of dispersive electromagnetic eigenvalue problems in two dimensions	1
Error bound and exact penalty method for optimization problems with nonnegative orthogonal constraint	1
A discontinuous least squares finite element method for time-harmonic Maxwell equations	1
The Kirchhoff plate equation on surfaces: the surface Hellan–Herrmann–Johnson method	1
A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity	1
Euler simulation of interacting particle systems and McKean–Vlasov SDEs with fully super-linear growth drifts in space and interaction	1
Convergence analysis of a numerical scheme for a tumour growth model	1
A sub-sampled tensor method for nonconvex optimization	1
A local energy-based discontinuous Galerkin method for fourth-order semilinear wave equations	1
A posteriori error estimates for fully coupled McKean–Vlasov forward-backward SDEs	1
Error analysis for a Crouzeix–Raviart approximation of the variable exponent Dirichlet problem	1
Efficient implementation of the exact artificial boundary condition for the exterior problem of the Stokes system in three dimensions	1
Nodal discrete duality numerical scheme for nonlinear diffusion problems on general meshes	1
Global and explicit approximation of piecewise-smooth two-dimensional functions from cell-average data	1
Finite difference schemes for a size structured coagulation-fragmentation model in the space of Radon measures	1
Analysis of a Galerkin finite element method for the Maxwell–Schrödinger system under temporal gauge	1
A second-order Magnus-type integrator for evolution equations with delay	1
Transfer of conservative discrete differential operators between staggered grids: construction and duality relations	1
Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method	1
Optimal convergence of arbitrary Lagrangian–Eulerian iso-parametric finite element methods for parabolic equations in an evolving domain	1
A pressure-robust HHO method for the solution of the incompressible Navier–Stokes equations on general meshes	1
Spurious solutions for high-order curl problems	1
A new step size selection strategy for the superiorization methodology using subgradient vectors and its application for solving convex constrained optimization problems	1
A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations	1
On the convergence of Broyden’s method and some accelerated schemes for singular problems	1
Convergence rate of inertial forward–backward algorithms based on the local error bound condition	1
Analysis of an electroless plating problem	1
Finite volumes for the Stefan–Maxwell cross-diffusion system	1
Maximum norm a posteriori error estimates for convection–diffusion problems	1
A second-order bulk–surface splitting for parabolic problems with dynamic boundary conditions	1
Improved structural methods for nonlinear differential-algebraic equations via combinatorial relaxation	1
Group sparse optimization for inpainting of random fields on the sphere	1
On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field	1
Divergence-conforming methods for transient double-diffusive flows: a priori and a posteriori error analysis	1
Linearly implicit energy-preserving integrating factor methods and convergence analysis for the 2D nonlinear Schrödinger equation with wave operator	1
Martingale product estimators for sensitivity analysis in computational statistical physics	1
The One Step Malliavin scheme: new discretization of BSDEs implemented with deep learning regressions	1
Numerical analysis of multiple scattering theory for electronic structure calculations	1
An a priori error analysis of adjoint-based super-convergent Galerkin approximations of linear functionals	1
Semilinear optimal control with Dirac measures	1
Maximum norm error bounds for the full discretization of nonautonomous wave equations	1
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs	1
Error estimates for the numerical approximation of optimal control problems with nonsmooth pointwise-integral control constraints	1
Convergent evolving finite element approximations of boundary evolution under shape gradient flow	1
On the necessity of the inf-sup condition for a mixed finite element formulation	1
The weak convergence order of two Euler-type discretization schemes for the log-Heston model	1
Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems	1
On the stability and convergence of discontinuous Galerkin schemes for incompressible flows	1
A novel spectral method for the semiclassical Schrödinger equation based on the Gaussian wave-packet transform	1
Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media	1
A matrix algebra approach to approximate Hessians	1
Pyramid transform of manifold data via subdivision operators	1
Convergence of preconditioned Hamiltonian Monte Carlo on Hilbert spaces	1
A linear implicit Euler method for the finite element discretization of a controlled stochastic heat equation	1
Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems	1
Plain convergence of adaptive algorithms without exploiting reliability and efficiency	1