Advances in Computational Mathematics

Article	Citations
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	41
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	29
The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers’ equation	28
The role of mesh quality and mesh quality indicators in the virtual element method	22
A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation	22
Persistence Curves: A canonical framework for summarizing persistence diagrams	20
Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations	19
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs	19
Virtual element methods for the three-field formulation of time-dependent linear poroelasticity	19
Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation	16
p- and hp- virtual elements for the Stokes problem	16
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method	15
A family of C1 quadrilateral finite elements	15
Structure-preserving interpolation of bilinear control systems	13
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	12
Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators	11
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	11
A rational RBF interpolation with conditionally positive definite kernels	11
A stable second-order BDF scheme for the three-dimensional Cahn–Hilliard–Hele–Shaw system	10
Randomized linear algebra for model reduction—part II: minimal residual methods and dictionary-based approximation	10
A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations	10
Space-time error estimates for deep neural network approximations for differential equations	10
A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation	9
Tensor completion via bilevel minimization with fixed-point constraint to estimate missing elements in noisy data	9
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	9

Kernel aggregated fast multipole method	8
Mixed precision path tracking for polynomial homotopy continuation	8
Joint spectral radius and ternary hermite subdivision	8
Learning via variably scaled kernels	8
A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model	8
Data-driven uncertainty quantification in macroscopic traffic flow models	8
A Grassmann manifold handbook: basic geometry and computational aspects	7
Balanced truncation of linear time-invariant systems over finite-frequency ranges	7
An adaptive discontinuous finite volume element method for the Allen-Cahn equation	7
The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers	7
An adaptive spectral graph wavelet method for PDEs on networks	7
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	7
Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations	7
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	7
New convergence analysis of a primal-dual algorithm with large stepsizes	7
A hybrid collocation-perturbation approach for PDEs with random domains	6
Exponential mean-square stability properties of stochastic linear multistep methods	6
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations	6
A quadratic finite volume method for nonlinear elliptic problems	6
On basis constructions in finite element exterior calculus	6
A stabilizer-free pressure-robust finite element method for the Stokes equations	6
Accurate computations with matrices related to bases {tieλt}	6
Approximation of functions from Korobov spaces by deep convolutional neural networks	6
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	6
Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems	6
Small errors imply large evaluation instabilities	6
A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampère equation	5
Unified construction and L2 analysis for the finite volume element method over tensorial meshes	5
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	5
Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering	5
Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds	5
High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation	5
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects	5
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	5
Stabilization of spline bases by extension	5
State-dependent Riccati equation feedback stabilization for nonlinear PDEs	5
Numerical algorithms for water waves with background flow over obstacles and topography	5
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	5
An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations	5
Clothoid fitting and geometric Hermite subdivision	5
Accurate singular values of a class of parameterized negative matrices	5
Symplectic geometry and connectivity of spaces of frames	5
Continuous window functions for NFFT	5
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations	5
A structure-preserving algorithm for surface water flows with transport processes	5
Tensor rank bounds for point singularities in ℝ3	4
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	4
Rapid evaluation of the spectral signal detection threshold and Stieltjes transform	4
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels	4
Edge detection with trigonometric polynomial shearlets	4

A new linearized fourth-order conservative compact difference scheme for the SRLW equations	4
Computing the reciprocal of a ϕ-function by rational approximation	4
An hp-version Legendre spectral collocation method for multi-order fractional differential equations	4
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	4
Adaptive and optimal pointwise deconvolution density estimations by wavelets	4
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	4
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	4
A new framework for polynomial approximation to differential equations	4
Comparison of integral equations for the Maxwell transmission problem with general permittivities	4
Cs-smooth isogeometric spline spaces over planar bilinear multi-patch parameterizations	4
A fast and oblivious matrix compression algorithm for Volterra integral operators	4
Limited memory restarted ℓp-ℓq minimization methods using generalized Krylov subspaces	4
Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements	4
A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law	4
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	4
Counting the dimension of splines of mixed smoothness	4
The hot spots conjecture can be false: some numerical examples	4
A generalisation of de la Vallée-Poussin procedure to multivariate approximations	4
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	4
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	4
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	4
Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials	4
A fast time domain solver for the equilibrium Dyson equation	4
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	4
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	4
A space-time certified reduced basis method for quasilinear parabolic partial differential equations	3
Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization	3
Convergence rates for boundedly regular systems	3
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	3
Linear multi-step methods and their numerical stability for solving gradient flow equations	3
Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes	3
Optimal control for a coupled spin-polarized current and magnetization system	3
A generalised complete flux scheme for anisotropic advection-diffusion equations	3
H2Opus: a distributed-memory multi-GPU software package for non-local operators	3
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes	3
Simultaneous identification of initial value and source strength in a transmission problem for a parabolic equation	3
An adaptive kernel-split quadrature method for parameter-dependent layer potentials	3
Explicit multivariate approximations from cell-average data	3
Robin-Robin domain decomposition methods for the dual-porosity-conduit system	3
High-order corrected trapezoidal rules for a class of singular integrals	3
Uniqueness of phase retrieval from three measurements	3
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	3
Sampling-free model reduction of systems with low-rank parameterization	3
Convergence of consistent and inconsistent schemes for fractional diffusion problems with boundaries	3
Reconstruction of low-rank aggregation kernels in univariate population balance equations	3
An inertial extragradient algorithm for equilibrium and generalized split null point problems	3
Simpler is better: a comparative study of randomized pivoting algorithms for CUR and interpolative decompositions	3
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations	3
Correction to: Exponential mean-square stability properties of stochastic linear multistep methods	3
Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations	3
A novel robust fractional-time anisotropic diffusion for multi-frame image super-resolution	3
Finding geodesics joining given points	3
An adaptive multiscale hybrid-mixed method for the Oseen equations	3
Estimating the error in matrix function approximations	3
Exponential tractability of L2-approximation with function values	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition	3
Newton’s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils	3
Mass- and energy-conserving Gauss collocation methods for the nonlinear Schrödinger equation with a wave operator	2
Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval	2
Two-scale finite element discretizations for nonlinear eigenvalue problems in quantum physics	2
Convergence analysis of oversampled collocation boundary element methods in 2D	2
Implicit finite volume method with a posteriori limiting for transport networks	2
Exponentially fitted methods with a local energy conservation law	2
Complex-scaled infinite elements for resonance problems in heterogeneous open systems	2
New low-order mixed finite element methods for linear elasticity	2
Non-symmetric isogeometric FEM-BEM couplings	2
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
A fast solver for elastic scattering from axisymmetric objects by boundary integral equations	2
Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems	2
Numerical analysis of a chemotaxis model for tumor invasion	2
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	2
Hessian discretisation method for fourth-order semi-linear elliptic equations: applications to the von Kármán and Navier–Stokes models	2
Numerical exponential decay of thermoelastic waves connected in parallel	2
A new approach to proper orthogonal decomposition with difference quotients	2
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	2
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	2

Adaptive sampling and modal expansions in pattern-forming systems	2
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	2
An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms	2
Carleman estimates and controllability results for fully discrete approximations of 1D parabolic equations	2
Max filtering with reflection groups	2
Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators	2
A second-order scheme based on blended BDF for the incompressible MHD system	2
Rectangular eigenvalue problems	2
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	2
Multivariate quadrature of a singular integrand	2
When is there a representer theorem?	2
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	2
Exact posterior computation for the binomial–Kumaraswamy model	2
The essence of invertible frame multipliers in scalability	2
Riemannian conjugate gradient method for low-rank tensor completion	2
Efficient function approximation on general bounded domains using splines on a Cartesian grid	2
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	1
Variational Bayesian inversion for the reaction coefficient in space-time nonlocal diffusion equations	1
A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction	1
On the balanced truncation error bound and sign parameters from arrowhead realizations	1
Semi-Lagrangian finite element exterior calculus for incompressible flows	1
Generalised Wendland functions for the sphere	1
Hermite interpolation by planar cubic-like ATPH	1
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	1
Convergence analysis of the scaled boundary finite element method for the Laplace equation	1
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	1
Extrapolated regularization of nearly singular integrals on surfaces	1
Linear/Ridge expansions: enhancing linear approximations by ridge functions	1
Interpolation of 3D data streams with C2 PH quintic splines	1
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	1
Solving the backward problem for time-fractional wave equations by the quasi-reversibility regularization method	1
Randomized continuous frames in time-frequency analysis	1
Weak approximation of SDEs for tempered distributions and applications	1
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	1
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	1
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	1
Supercloseness analysis of a stabilizer-free weak Galerkin finite element method for viscoelastic wave equations with variable coefficients	1
A mixed virtual element method for nearly incompressible linear elasticity equations	1
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	1
Adaptive and local regularization for data fitting by tensor-product spline surfaces	1
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals	1
An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	1
$$\mathcal {H}$$-inverses for RBF interpolation	1
New degrees of freedom for differential forms on cubical meshes	1
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	1
Optimized Ventcel-Schwarz methods for the Cahn-Hilliard equation discretized by the stabilized linear Crank-Nicolson scheme	1
Polynomial spline spaces of non-uniform bi-degree on T-meshes: combinatorial bounds on the dimension	1
Riemannian optimization for phase retrieval from masked Fourier measurements	1
Phase retrieval and system identification in dynamical sampling via Prony’s method	1
Numerical computation of a preimage domain for an infinite strip with rectilinear slits	1
A fractional osmosis model for image fusion	1
Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem	1
Stokes equations under Tresca friction boundary condition: a truncated approach	1
A multilevel Newton’s method for the Steklov eigenvalue problem	1
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	1
A high-order algorithm for time-domain scattering in three dimensions	1
$${\mathcal{H}}$$-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations	1
One-step optimization method for equilibrium problems	1
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	1
Fast gradient methods for uniformly convex and weakly smooth problems	1
Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization	1
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	1
Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction	1
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	1
Inexact GMRES iterations and relaxation strategies with fast-multipole boundary element method	1
Numerical analysis of nonlinear degenerate parabolic problems with application to eddy current models	1
Half-quadratic alternating direction method of multipliers for robust orthogonal tensor approximation	1
On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems	1
A theoretical study of a bilateral term with a tensor-based fourth-order PDE for image super-resolution	1
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification	1
Error bounds for a least squares meshless finite difference method on closed manifolds	1
A DCA-Newton method for quartic minimization over the sphere	1
Interaction with an obstacle in the 2D focusing nonlinear Schrödinger equation	1
Directional wavelet packets originating from polynomial splines	1
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	1
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	1