Advances in Computational Mathematics

Article	Citations
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	233
Exponential decay and numerical treatment for mixture problem with Fourier law and frictional damping	82
Data-driven uncertainty quantification in macroscopic traffic flow models	61
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	26
A low-rank neural representation of entropy solutions	23
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	21
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	20
Variational methods for solving numerically magnetostatic systems	17
Dictionary-based model reduction for state estimation	17
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	17
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	16
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	15
Averaging property of wedge product and naturality in discrete exterior calculus	15
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	15
Stable least-squares space-time boundary element methods for the wave equation	14
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	14
A new magnetic-coupled binary phase-field crystal model and its efficient fully discrete decoupled energy-stable scheme	13
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	13
Smoothed distance kernels for MMDs and applications in Wasserstein gradient flows	13
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
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	11
Stray field computation by inverted finite elements: a new method in micromagnetic simulations	10
Weak approximation of SDEs for tempered distributions and applications	10
Randomized GCUR decompositions	10

Adaptive quarklet tree approximation	10
Two-level discretization of the 3D stationary Navier–Stokes equations with damping based on a difference finite element method	10
Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem	10
Toward a certified greedy Loewner framework with minimal sampling	10
A method of fundamental solutions for large-scale 3D elastance and mobility problems	9
Accurate computations with matrices related to bases {tieλt}	9
Approximation in the extended functional tensor train format	9
Max filtering with reflection groups	9
Splitting scheme for backward doubly stochastic differential equations	9
Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization	9
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	9
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations	9
Adaptive and local regularization for data fitting by tensor-product spline surfaces	9
Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations	8
SVD-based algorithms for tensor wheel decomposition	8
Analyzing the function $$z\uparrow \uparrow \!a$$ for fractional a	7
A fast time domain solver for the equilibrium Dyson equation	7
A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations	7
On a non-uniform $$\alpha $$-robust IMEX-L1 mixed FEM for time-fractional PIDEs	7
Anderson acceleration of a Picard solver for the Oldroyd-B model of viscoelastic fluids	7
A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem	7
Energy-stable and efficient finite element schemes for the Shliomis model of ferrofluid flows	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
Uniform error bounds of a nested Picard iterative integrator for the Klein-Gordon-Zakharov system in the subsonic limit regime	7
An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM	7
$$\mathcal {H}_2$$ optimal rational approximation on general domains	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
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	6
A posteriori virtual element method for the acoustic vibration problem	6
An adaptive finite element DtN method for the acoustic-elastic interaction problem	6
A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators	6
On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems	6
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	6
Analysis of the geometric structure of neural networks and neural ODEs via morse functions	6
Error estimates for mixed and hybrid FEM for elliptic optimal control problems with penalizations	6
A SUPG-stabilized virtual element method for the Navier–Stokes equation: approximations of branches of non-singular solutions	6
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	6
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus	6
Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media	5
Constrained rational fitting for $$\mathcal {D}$$-stable model order reduction	5
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	5
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems	5
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	5
Frame-normalizable sequences	5
Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles	5
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies	5
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	5
A second-order scheme based on blended BDF for the incompressible MHD system	5

Approximation of functions from Korobov spaces by deep convolutional neural networks	5
Tight frames over the quaternions and equiangular lines	5
Generalised Wendland functions for the sphere	5
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields	5
On a deterministic block Kaczmarz-type method and its acceleration for the solution of large-scale linear systems	5
High-order corrected trapezoidal rules for a class of singular integrals	5
A conforming virtual element method for Emden-Fowler model over polygonal meshes	5
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	4
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	4
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	4
Correction: A posteriori virtual element method for the acoustic vibration problem	4
A scaling fractional asymptotical regularization method for linear inverse problems	4
GP-CMRH: an inner product free iterative method for block two-by-two nonsymmetric linear systems	4
A block-randomized stochastic method with importance sampling for CP tensor decomposition	4
Approximation of curve-based sleeve functions in high dimensions	4
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology	4
Error analysis of a hybrid numerical method for optimal control problem governed by parabolic PDEs in random cylindrical domains	4
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	4
Exponentially fitted methods with a local energy conservation law	4
Obstructions for Gabor frames of the second-order B-spline	4
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	4
A mixed virtual element method for nearly incompressible linear elasticity equations	4
An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	4
Spatially semi-discretely uniformly exponential stability approximation for one-dimensional thermoelastic system	4
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	4
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform	4
Which transmission condition is the best in optimized Schwarz waveform relaxation for viscoelastic equation: Robin or characteristic?	4
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	4
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	4
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	4
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	4
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	4
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	4
A generalized quasi-reversibility regularization method to determine a spatial source component in a time-fractional diffusion-wave equation	4
A direct parallel-in-time finite difference solver for quenching combustion problem	4
On convergence of the generalized Lanczos trust-region method for trust-region subproblems	4
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations	4
Stabilized gradient flow schemes of phase field model for shape and topology optimization in diffusion	4
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	4
Low-rank exponential integrators for stiff differential Riccati equations	4
A new approach to proper orthogonal decomposition with difference quotients	4
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	3
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	3
A comparative numerical study of spectral properties in isogeometric collocation and Galerkin methods for acoustic waves	3
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	3
Data-driven optimal approximation on Hardy spaces in simply connected domains	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
A variable time-step IMEX BDF2 scheme for the incompressible MHD system	3
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	3
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	3
Solving elliptic optimal control problems via neural networks and optimality system	3
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	3
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	3
Curve fitting on a quantum annealer for an advanced navigation method	3
Exponential tractability of L2-approximation with function values	3
An optimal ansatz space for moving least squares approximation on spheres	3
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	3
Developing and analyzing some new finite element methods for a non-local hydrodynamic Drude model	3
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	3
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	3
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential 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
Balanced truncation for quadratic-bilinear control systems	3
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	3
Decoupled weak Galerkin finite element method for Maxwell’s equations	3
Space-time error estimates for deep neural network approximations for differential equations	3
Numerical methods for forward fractional Feynman–Kac equation	3
A primal-dual adaptive finite element method for total variation minimization	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
A sparse approximation for fractional Fourier transform	3
Nonconforming virtual element method for general second-order elliptic problems on curved domain	3
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	3
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Local behaviors of Fourier expansions for functions of limited regularities	2
Correction to: Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	2
Limitations of neural network training due to numerical instability of backpropagation	2
New low-order mixed finite element methods for linear elasticity	2

Convergence of projected subgradient method with sparse or low-rank constraints	2
Error bounds for a least squares meshless finite difference method on closed manifolds	2
Explicit multivariate approximations from cell-average data	2
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	2
A high-order algorithm for time-domain scattering in three dimensions	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2
Efficient computation of the sinc matrix function for the integration of second-order differential equations	2
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	2
Optimal compactly supported functions in Sobolev spaces	2
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	2
An adaptive finite element DtN method for the acoustic-elastic interaction problem in periodic structures	2
A two-grid method with dispersion matching for finite-element Helmholtz problems	2
Matching pursuit with unbounded parameter domains	2
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	2
Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation	2
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	2
A discretization theory of meshfree collocation for nonlinear systems of partial differential equations	2
Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem	2
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	2
Online identification and control of PDEs via reinforcement learning methods	2
On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation	2
Stable approximate evaluation of unbounded matrix operator and its application to an inverse problem	2
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	2
A posteriori error estimates for wave maps into spheres	2
Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback controller design	2
Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation	2
A stochastic perturbation analysis of the QR decomposition and its applications	2
An inertial extragradient algorithm for equilibrium and generalized split null point problems	2
On the asymptotically compatible energies of L1 and L1-SAV schemes for time-fractional Allen-Cahn model	2
An interpolation–regression approach for function approximation on the disk and its application to cubature formulas	2
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	2
A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	2
Robust kernel-based gradient descent with random features	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction	2
Chebyshev accelerating technique for solving generalized non-symmetric eigenvalue problems	2
Strong convergence of linear implicit virtual element methods for the nonlinear stochastic parabolic equation with multiplicative noise	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2
Numerical analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions	2
The $$L_q$$-weighted dual programming of the linear Chebyshev approximation and an interior-point method	2
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	2
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem	2
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	2