Advances in Computational Mathematics

Article	Citations
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	122
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	54
Dictionary-based model reduction for state estimation	33
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	30
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	27
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals	16
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	16
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	16
Variational methods for solving numerically magnetostatic systems	14
Tensor rank bounds for point singularities in ℝ3	14
Data-driven uncertainty quantification in macroscopic traffic flow models	13
Averaging property of wedge product and naturality in discrete exterior calculus	13
Exponential decay and numerical treatment for mixture problem with Fourier law and frictional damping	13
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	13
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	12
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	12
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	12
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	12
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	11
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	11
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	10
Implicit finite volume method with a posteriori limiting for transport networks	10
Uniqueness of phase retrieval from three measurements	10
Weak approximation of SDEs for tempered distributions and applications	10
Max filtering with reflection groups	9

An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	9
Adaptive quarklet tree approximation	9
Stray field computation by inverted finite elements: a new method in micromagnetic simulations	9
Toward a certified greedy Loewner framework with minimal sampling	8
Accurate computations with matrices related to bases {tieλt}	8
SVD-based algorithms for tensor wheel decomposition	8
Randomized GCUR decompositions	8
Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations	8
An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms	8
Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem	8
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations	8
A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction	8
On a non-uniform $$\alpha $$-robust IMEX-L1 mixed FEM for time-fractional PIDEs	7
A fast time domain solver for the equilibrium Dyson equation	7
Randomized continuous frames in time-frequency analysis	7
Splitting scheme for backward doubly stochastic differential equations	7
Adaptive and local regularization for data fitting by tensor-product spline surfaces	7
A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem	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 fast and oblivious matrix compression algorithm for Volterra integral operators	7
Approximation in the extended functional tensor train format	7
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	7
A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations	6
A hybrid boundary integral-PDE approach for the approximation of the demagnetization potential in micromagnetics	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
On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems	6
Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul’yev methods	6
Error estimates for mixed and hybrid FEM for elliptic optimal control problems with penalizations	6
An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM	6
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	6
A SUPG-stabilized virtual element method for the Navier–Stokes equation: approximations of branches of non-singular solutions	6
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
Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media	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
Generalised Wendland functions for the sphere	5
Uniform error bounds of a nested Picard iterative integrator for the Klein-Gordon-Zakharov system in the subsonic limit regime	5
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields	5
$$\mathcal {H}_2$$ optimal rational approximation on general domains	5
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	5
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	4
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	4
A second-order scheme based on blended BDF for the incompressible MHD system	4
Approximation of curve-based sleeve functions in high dimensions	4

One-step optimization method for equilibrium problems	4
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform	4
High-order corrected trapezoidal rules for a class of singular integrals	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
Frame-normalizable sequences	4
Correction: A posteriori virtual element method for the acoustic vibration problem	4
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	4
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	4
A scaling fractional asymptotical regularization method for linear inverse problems	4
A rational RBF interpolation with conditionally positive definite kernels	4
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	4
Fast gradient methods for uniformly convex and weakly smooth problems	4
Approximation of functions from Korobov spaces by deep convolutional neural networks	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
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems	4
A block-randomized stochastic method with importance sampling for CP tensor decomposition	4
H2Opus: a distributed-memory multi-GPU software package for non-local operators	3
Optimal control for a coupled spin-polarized current and magnetization system	3
A sparse approximation for fractional Fourier transform	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
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	3
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	3
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	3
An alternative approach for order conditions of Runge-Kutta-Nyström methods	3
Mixed precision path tracking for polynomial homotopy continuation	3
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	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
Comparison of integral equations for the Maxwell transmission problem with general permittivities	3
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	3
A new approach to proper orthogonal decomposition with difference quotients	3
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	3
Exponential tractability of L2-approximation with function values	3
Obstructions for Gabor frames of the second-order B-spline	3
Persistence Curves: A canonical framework for summarizing persistence diagrams	3
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	3
Numerical methods for forward fractional Feynman–Kac equation	3
A mixed virtual element method for nearly incompressible linear elasticity equations	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations	3
An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	3
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	3
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	3
A primal-dual adaptive finite element method for total variation minimization	3
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	3
Decoupled weak Galerkin finite element method for Maxwell’s equations	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	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
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	3
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	3
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber	3
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	3
The hot spots conjecture can be false: some numerical examples	3
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	2
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2
Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem	2
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	2
A family of C1 quadrilateral finite elements	2
A stochastic perturbation analysis of the QR decomposition and its applications	2
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	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
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	2
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	2
Explicit multivariate approximations from cell-average data	2
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes	2
Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction	2
Error bounds for a least squares meshless finite difference method on closed manifolds	2
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	2
New low-order mixed finite element methods for linear elasticity	2
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	2

A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	2
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	2
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	2
An optimal ansatz space for moving least squares approximation on spheres	2
Space-time error estimates for deep neural network approximations for differential equations	2
Balanced truncation for quadratic-bilinear control systems	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	2
Online identification and control of PDEs via reinforcement learning methods	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
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	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
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
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Nonconforming virtual element method for general second-order elliptic problems on curved domain	2
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	2
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	2
Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators	2
Accurate singular values of a class of parameterized negative matrices	2
On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation	2
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	2
An inertial extragradient algorithm for equilibrium and generalized split null point problems	2