Advances in Computational Mathematics

Article	Citations
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation	39
Simple maximum principle preserving time-stepping methods for time-fractional Allen-Cahn equation	26
Optimal H1 spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation	23
The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers’ equation	23
A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation	21
The role of mesh quality and mesh quality indicators in the virtual element method	18
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs	17
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	16
Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation	16
Persistence Curves: A canonical framework for summarizing persistence diagrams	16
Virtual element methods for the three-field formulation of time-dependent linear poroelasticity	16
Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations	14
p- and hp- virtual elements for the Stokes problem	14
A unified analysis of a class of quadratic finite volume element schemes on triangular meshes	13
Multigrid preconditioners for anisotropic space-fractional diffusion equations	13
High-order cut finite elements for the elastic wave equation	12
A family of C1 quadrilateral finite elements	12
Analysis of adaptive synchrosqueezing transform with a time-varying parameter	11
Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators	11
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method	11
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	10
A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations	10
Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations	9
Structure-preserving interpolation of bilinear control systems	9
Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation	9

A mixed virtual element method for the vibration problem of clamped Kirchhoff plate	9
A rational RBF interpolation with conditionally positive definite kernels	9
Generalized Born-Jordan distributions and applications	9
A stable second-order BDF scheme for the three-dimensional Cahn–Hilliard–Hele–Shaw system	9
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	9
Joint spectral radius and ternary hermite subdivision	8
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	8
Space-time error estimates for deep neural network approximations for differential equations	8
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	8
A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model	8
An integral equation–based numerical method for the forced heat equation on complex domains	8
Trefftz discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport	8
Mixed precision path tracking for polynomial homotopy continuation	8
Learning via variably scaled kernels	8
A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction	8
Accelerated hybrid methods for solving pseudomonotone equilibrium problems	7
Data-driven uncertainty quantification in macroscopic traffic flow models	7
Tensor completion via bilevel minimization with fixed-point constraint to estimate missing elements in noisy data	7
Solving partial differential equations on (evolving) surfaces with radial basis functions	7
An adaptive spectral graph wavelet method for PDEs on networks	7
Hankel-norm approximation of large-scale descriptor systems	7
Adaptive hybridizable discontinuous Galerkin methods for nonstationary convection diffusion problems	6
A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation	6
Least-Squares Padé approximation of parametric and stochastic Helmholtz maps	6
Randomized linear algebra for model reduction—part II: minimal residual methods and dictionary-based approximation	6
Kernel aggregated fast multipole method	6
Frames and weak frames for unbounded operators	6
New convergence analysis of a primal-dual algorithm with large stepsizes	6
Virtual element methods for nonlocal parabolic problems on general type of meshes	6
Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems	6
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	6
Exponential mean-square stability properties of stochastic linear multistep methods	5
Balanced truncation of linear time-invariant systems over finite-frequency ranges	5
The hot spots conjecture can be false: some numerical examples	5
A hybrid collocation-perturbation approach for PDEs with random domains	5
An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations	5
A quadratic finite volume method for nonlinear elliptic problems	5
Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering	5
A structure-preserving algorithm for surface water flows with transport processes	5
Fast randomized matrix and tensor interpolative decomposition using CountSketch	5
A characterization of supersmoothness of multivariate splines	5
Numerical algorithms for water waves with background flow over obstacles and topography	5
Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds	4
Continuous window functions for NFFT	4
Counting the dimension of splines of mixed smoothness	4
An hp-version of the C0-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems	4
Unconditionally optimal convergence analysis of second-order BDF Galerkin finite element scheme for a hybrid MHD system	4
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	4
Computing the reciprocal of a ϕ-function by rational approximation	4
Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements	4

Cs-smooth isogeometric spline spaces over planar bilinear multi-patch parameterizations	4
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels	4
Stabilization of spline bases by extension	4
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	4
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	4
High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation	4
A fast and oblivious matrix compression algorithm for Volterra integral operators	4
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	4
Edge detection with trigonometric polynomial shearlets	4
Clothoid fitting and geometric Hermite subdivision	4
The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers	4
Difference potentials method for models with dynamic boundary conditions and bulk-surface problems	4
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	4
Symplectic geometry and connectivity of spaces of frames	4
A boundary-partition-based Voronoi diagram of d-dimensional balls: definition, properties, and applications	4
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	4
Tensor rank bounds for point singularities in ℝ3	4
Determination of temperature distribution and thermal flux for two-dimensional inhomogeneous sideways heat equations	4
Structured backward error analysis for generalized saddle point problems	4
A generalisation of de la Vallée-Poussin procedure to multivariate approximations	4
A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampère equation	4
Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations	4
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations	4
Unified construction and L2 analysis for the finite volume element method over tensorial meshes	4
Comparison of integral equations for the Maxwell transmission problem with general permittivities	4
Accurate singular values of a class of parameterized negative matrices	4
Linear multi-step methods and their numerical stability for solving gradient flow equations	3
A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law	3
On basis constructions in finite element exterior calculus	3
Adaptive and optimal pointwise deconvolution density estimations by wavelets	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
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	3
Newton’s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils	3
Accurate computations with matrices related to bases {tieλt}	3
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	3
Approximation of functions from Korobov spaces by deep convolutional neural networks	3
Finding geodesics joining given points	3
Limited memory restarted ℓp-ℓq minimization methods using generalized Krylov subspaces	3
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	3
A stabilizer-free pressure-robust finite element method for the Stokes equations	3
Local superconvergence of post-processed high-order finite volume element solutions	3
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	3
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	3
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	3
Convergence rates for boundedly regular systems	3
State-dependent Riccati equation feedback stabilization for nonlinear PDEs	3
An hp-version Legendre spectral collocation method for multi-order fractional differential equations	3
Reconstruction of low-rank aggregation kernels in univariate population balance equations	3
Rapid evaluation of the spectral signal detection threshold and Stieltjes transform	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
An inertial extragradient algorithm for equilibrium and generalized split null point problems	3
An overlapping domain decomposition framework without dual formulation for variational imaging problems	3
An adaptive kernel-split quadrature method for parameter-dependent layer potentials	3
Correction to: Exponential mean-square stability properties of stochastic linear multistep methods	3
Robin-Robin domain decomposition methods for the dual-porosity-conduit system	3
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations	3
Optimal control for a coupled spin-polarized current and magnetization system	2
Estimating the error in matrix function approximations	2
A fast time domain solver for the equilibrium Dyson equation	2
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	2
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects	2
Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes	2
Numerical analysis of a finite element method for the electromagnetic concentrator model	2
Multivariate quadrature of a singular integrand	2
Small errors imply large evaluation instabilities	2
Convergence of consistent and inconsistent schemes for fractional diffusion problems with boundaries	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2
A sparse FFT approach for ODE with random coefficients	2
An adaptive discontinuous finite volume element method for the Allen-Cahn equation	2
Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval	2
Convergence analysis of oversampled collocation boundary element methods in 2D	2
Implicit finite volume method with a posteriori limiting for transport networks	2
Adaptive sampling and modal expansions in pattern-forming systems	2
Rectangular eigenvalue problems	2
The essence of invertible frame multipliers in scalability	2
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	2
Non-symmetric isogeometric FEM-BEM couplings	2
Sampling-free model reduction of systems with low-rank parameterization	2
Spectral collocation method for nonlinear Caputo fractional differential system	2

A generalised complete flux scheme for anisotropic advection-diffusion equations	2
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	2
A fast solver for elastic scattering from axisymmetric objects by boundary integral equations	2
A space-time certified reduced basis method for quasilinear parabolic partial differential equations	2
Carleman estimates and controllability results for fully discrete approximations of 1D parabolic equations	2
Superconvergent gradient recovery for nonlinear Poisson-Nernst-Planck equations with applications to the ion channel problem	2
Numerical analysis of a chemotaxis model for tumor invasion	2
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	2
When is there a representer theorem?	2
Uniqueness of phase retrieval from three measurements	2
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	2
An adaptive multiscale hybrid-mixed method for the Oseen equations	2
Exact posterior computation for the binomial–Kumaraswamy model	2
Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow	2
On the computation of Nash and Pareto equilibria for some bi-objective control problems for the wave equation	2
Exponential tractability of L2-approximation with function values	2
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	2
H2Opus: a distributed-memory multi-GPU software package for non-local operators	2
An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Max filtering with reflection groups	2
Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization	2
Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators	2
HT-AWGM: a hierarchical Tucker–adaptive wavelet Galerkin method for high-dimensional elliptic problems	2