Advances in Computational Mathematics

Article	Citations
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	166
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	61
Dictionary-based model reduction for state estimation	38
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	32
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	31
Exponential decay and numerical treatment for mixture problem with Fourier law and frictional damping	20
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	19
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	18
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	15
Variational methods for solving numerically magnetostatic systems	15
Tensor rank bounds for point singularities in ℝ3	15
Data-driven uncertainty quantification in macroscopic traffic flow models	14
Averaging property of wedge product and naturality in discrete exterior calculus	14
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	13
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	13
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	13
Implicit finite volume method with a posteriori limiting for transport networks	12
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	11
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	11
Uniqueness of phase retrieval from three measurements	11
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	11
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	11
Weak approximation of SDEs for tempered distributions and applications	11
Adaptive quarklet tree approximation	10
Stray field computation by inverted finite elements: a new method in micromagnetic simulations	10

Two-level discretization of the 3D stationary Navier–Stokes equations with damping based on a difference finite element method	10
Randomized GCUR decompositions	9
A method of fundamental solutions for large-scale 3D elastance and mobility problems	9
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	9
Toward a certified greedy Loewner framework with minimal sampling	9
Max filtering with reflection groups	9
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations	8
Splitting scheme for backward doubly stochastic differential equations	8
A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction	8
Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem	8
Adaptive and local regularization for data fitting by tensor-product spline surfaces	7
Accurate computations with matrices related to bases {tieλt}	7
Randomized continuous frames in time-frequency analysis	7
A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem	7
A SUPG-stabilized virtual element method for the Navier–Stokes equation: approximations of branches of non-singular solutions	7
Approximation in the extended functional tensor train format	7
Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations	7
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	7
On a non-uniform $$\alpha $$-robust IMEX-L1 mixed FEM for time-fractional PIDEs	7
Energy-stable and efficient finite element schemes for the Shliomis model of ferrofluid flows	7
SVD-based algorithms for tensor wheel decomposition	7
Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization	7
Simultaneous identification of initial value and source strength in a transmission problem for a parabolic equation	7
The role of mesh quality and mesh quality indicators in the virtual element method	7
A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations	7
A fast time domain solver for the equilibrium Dyson equation	7
An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM	6
A hybrid boundary integral-PDE approach for the approximation of the demagnetization potential in micromagnetics	6
An adaptive finite element DtN method for the acoustic-elastic interaction problem	6
Error estimates for mixed and hybrid FEM for elliptic optimal control problems with penalizations	6
On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems	6
A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators	6
Uniform error bounds of a nested Picard iterative integrator for the Klein-Gordon-Zakharov system in the subsonic limit regime	6
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	6
Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul’yev methods	6
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies	5
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields	5
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus	5
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	5
Generalised Wendland functions for the sphere	5
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	5
Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media	5
$$\mathcal {H}_2$$ optimal rational approximation on general domains	5
Frame-normalizable sequences	5
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	5
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	5
A posteriori virtual element method for the acoustic vibration problem	5
On convergence of the generalized Lanczos trust-region method for trust-region subproblems	5
Fast gradient methods for uniformly convex and weakly smooth problems	5
A scaling fractional asymptotical regularization method for linear inverse problems	4

Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	4
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations	4
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	4
Numerical analysis of a chemotaxis model for tumor invasion	4
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	4
Approximation of functions from Korobov spaces by deep convolutional neural networks	4
High-order corrected trapezoidal rules for a class of singular integrals	4
A second-order scheme based on blended BDF for the incompressible MHD system	4
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	4
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	4
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	4
Low-rank exponential integrators for stiff differential Riccati equations	4
The hot spots conjecture can be false: some numerical examples	4
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	4
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	4
Tight frames over the quaternions and equiangular lines	4
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations	4
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology	4
Correction: A posteriori virtual element method for the acoustic vibration problem	4
Error analysis of a hybrid numerical method for optimal control problem governed by parabolic PDEs in random cylindrical domains	4
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	4
An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	4
A block-randomized stochastic method with importance sampling for CP tensor decomposition	4
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform	4
Approximation of curve-based sleeve functions in high dimensions	4
One-step optimization method for equilibrium problems	4
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems	4
A conforming virtual element method for Emden-Fowler model over polygonal meshes	4
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	3
Space-time error estimates for deep neural network approximations for differential equations	3
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
A primal-dual adaptive finite element method for total variation minimization	3
Exponentially fitted methods with a local energy conservation law	3
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	3
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	3
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	3
Obstructions for Gabor frames of the second-order B-spline	3
Numerical methods for forward fractional Feynman–Kac equation	3
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	3
Persistence Curves: A canonical framework for summarizing persistence diagrams	3
An optimal ansatz space for moving least squares approximation on spheres	3
Nonconforming virtual element method for general second-order elliptic problems on curved domain	3
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	3
A new approach to proper orthogonal decomposition with difference quotients	3
A sparse approximation for fractional Fourier transform	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
Exponential tractability of L2-approximation with function values	3
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	3
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	3
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	3
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	3
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber	3
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	3
Balanced truncation for quadratic-bilinear control systems	3
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	3
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	3
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	3
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
Developing and analyzing some new finite element methods for a non-local hydrodynamic Drude model	3
H2Opus: a distributed-memory multi-GPU software package for non-local operators	3
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	3
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	3
A mixed virtual element method for nearly incompressible linear elasticity equations	3
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	3
Optimal control for a coupled spin-polarized current and magnetization system	3
Decoupled weak Galerkin finite element method for Maxwell’s equations	3
Computing the action of the matrix generating function of Bernoulli polynomials on a vector with an application to non-local boundary value problems	3
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	2
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	2
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	2
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	2
Error bounds for a least squares meshless finite difference method on closed manifolds	2
Local behaviors of Fourier expansions for functions of limited regularities	2
The essence of invertible frame multipliers in scalability	2
An optimal control framework for adaptive neural ODEs	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2

Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	2
A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	2
Limitations of neural network training due to numerical instability of backpropagation	2
Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction	2
Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem	2
Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation	2
A stochastic perturbation analysis of the QR decomposition and its applications	2
New low-order mixed finite element methods for linear elasticity	2
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	2
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	2
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	2
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	2
A posteriori error estimates for wave maps into spheres	2
On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation	2
Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback controller design	2
Stable approximate evaluation of unbounded matrix operator and its application to an inverse problem	2
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem	2
Convergence of projected subgradient method with sparse or low-rank constraints	2
Online identification and control of PDEs via reinforcement learning methods	2
Matching pursuit with unbounded parameter domains	2
Correction to: Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	2
An inertial extragradient algorithm for equilibrium and generalized split null point problems	2
Solving elliptic optimal control problems via neural networks and optimality system	2
A two-grid method with dispersion matching for finite-element Helmholtz problems	2
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	2
Robust kernel-based gradient descent with random features	2
Numerical analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions	2
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	2
The $$L_q$$-weighted dual programming of the linear Chebyshev approximation and an interior-point method	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	2
A high-order algorithm for time-domain scattering in three dimensions	2
Explicit multivariate approximations from cell-average data	2
An adaptive finite element DtN method for the acoustic-elastic interaction problem in periodic structures	2
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	2
Efficient computation of the sinc matrix function for the integration of second-order differential equations	2
An interpolation–regression approach for function approximation on the disk and its application to cubature formulas	2
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	2