Advances in Computational Mathematics

Article	Citations
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	138
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	56
Dictionary-based model reduction for state estimation	33
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	30
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	30
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	18
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	18
Exponential decay and numerical treatment for mixture problem with Fourier law and frictional damping	17
Data-driven uncertainty quantification in macroscopic traffic flow models	16
Tensor rank bounds for point singularities in ℝ3	13
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	13
Averaging property of wedge product and naturality in discrete exterior calculus	13
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	13
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	13
Variational methods for solving numerically magnetostatic systems	13
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	12
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	11
Implicit finite volume method with a posteriori limiting for transport networks	11
Uniqueness of phase retrieval from three measurements	11
Weak approximation of SDEs for tempered distributions and applications	10
Adaptive quarklet tree approximation	10
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	10
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	10
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	10
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	10

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

An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	4
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations	4
Numerical analysis of a chemotaxis model for tumor invasion	4
A scaling fractional asymptotical regularization method for linear inverse problems	4
One-step optimization method for equilibrium problems	4
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	4
Approximation of functions from Korobov spaces by deep convolutional neural networks	4
Comparison of integral equations for the Maxwell transmission problem with general permittivities	4
Fast gradient methods for uniformly convex and weakly smooth problems	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
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	4
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	4
Frame-normalizable sequences	4
The hot spots conjecture can be false: some numerical examples	4
High-order corrected trapezoidal rules for a class of singular integrals	4
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	4
A second-order scheme based on blended BDF for the incompressible MHD system	4
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	4
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology	4
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	3
Exponentially fitted methods with a local energy conservation law	3
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	3
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	3
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	3
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	3
Error analysis of a hybrid numerical method for optimal control problem governed by parabolic PDEs in random cylindrical domains	3
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations	3
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	3
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber	3
Nonconforming virtual element method for general second-order elliptic problems on curved domain	3
Space-time error estimates for deep neural network approximations for differential equations	3
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	3
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	3
An optimal ansatz space for moving least squares approximation on spheres	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
A primal-dual adaptive finite element method for total variation minimization	3
H2Opus: a distributed-memory multi-GPU software package for non-local operators	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
Exponential tractability of L2-approximation with function values	3
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	3
Persistence Curves: A canonical framework for summarizing persistence diagrams	3
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	3
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	3
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	3
Optimal control for a coupled spin-polarized current and magnetization system	3
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
A sparse approximation for fractional Fourier transform	3
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	3
Decoupled weak Galerkin finite element method for Maxwell’s equations	3
A new approach to proper orthogonal decomposition with difference quotients	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	3
A mixed virtual element method for nearly incompressible linear elasticity equations	3
Numerical methods for forward fractional Feynman–Kac equation	3
Obstructions for Gabor frames of the second-order B-spline	3
Low-rank exponential integrators for stiff differential Riccati equations	3
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	3
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	3
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	3
A family of C1 quadrilateral finite elements	3
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	3
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	3
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	3
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	2
A stochastic perturbation analysis of the QR decomposition and its applications	2
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	2
An adaptive finite element DtN method for the acoustic-elastic interaction problem in periodic structures	2
Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation	2
Limitations of neural network training due to numerical instability of backpropagation	2
Numerical analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions	2
Local behaviors of Fourier expansions for functions of limited regularities	2
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	2
Stable approximate evaluation of unbounded matrix operator and its application to an inverse problem	2
Error bounds for a least squares meshless finite difference method on closed manifolds	2
Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem	2
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2

Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	2
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	2
A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	2
Convergence of projected subgradient method with sparse or low-rank constraints	2
A two-grid method with dispersion matching for finite-element Helmholtz problems	2
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem	2
Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2
An inertial extragradient algorithm for equilibrium and generalized split null point problems	2
On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	2
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	2
Correction to: Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	2
Solving elliptic optimal control problems via neural networks and optimality system	2
The essence of invertible frame multipliers in scalability	2
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	2
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	2
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	2
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	2
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	2
Matching pursuit with unbounded parameter domains	2
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes	2
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	2
Explicit multivariate approximations from cell-average data	2
Computing the action of the matrix generating function of Bernoulli polynomials on a vector with an application to non-local boundary value problems	2
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	2
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	2
Balanced truncation for quadratic-bilinear control systems	2
Online identification and control of PDEs via reinforcement learning methods	2
New low-order mixed finite element methods for linear elasticity	2
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	2