Advances in Computational Mathematics

Article	Citations
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	268
Exponential decay and numerical treatment for mixture problem with Fourier law and frictional damping	87
Data-driven uncertainty quantification in macroscopic traffic flow models	69
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	26
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	25
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	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	19
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	19
A low-rank neural representation of entropy solutions	18
Dictionary-based model reduction for state estimation	17
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	16
Averaging property of wedge product and naturality in discrete exterior calculus	16
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	15
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	15
Uniqueness of phase retrieval from three measurements	14
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	14
Smoothed distance kernels for MMDs and applications in Wasserstein gradient flows	14
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	14
Stable least-squares space-time boundary element methods for the wave equation	12
Weak approximation of SDEs for tempered distributions and applications	11
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	11
Theoretical and numerical analysis of a nonlinear double-phase variable exponent model for image contrast enhancement	11
A new magnetic-coupled binary phase-field crystal model and its efficient fully discrete decoupled energy-stable scheme	11
Adaptive quarklet tree approximation	11

Toward a certified greedy Loewner framework with minimal sampling	10
Randomized GCUR decompositions	10
Two-level discretization of the 3D stationary Navier–Stokes equations with damping based on a difference finite element method	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	10
Max filtering with reflection groups	10
Stray field computation by inverted finite elements: a new method in micromagnetic simulations	10
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations	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
A method of fundamental solutions for large-scale 3D elastance and mobility problems	9
Analyzing the function $$z\uparrow \uparrow \!a$$ for fractional a	9
Approximation in the extended functional tensor train format	8
Nested operator inference for adaptive data-driven learning of reduced-order models	8
SVD-based algorithms for tensor wheel decomposition	8
Anderson acceleration of a Picard solver for the Oldroyd-B model of viscoelastic fluids	8
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	7
Simultaneous identification of initial value and source strength in a transmission problem for a parabolic equation	7
An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM	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
Adaptive and local regularization for data fitting by tensor-product spline surfaces	7
Energy-stable and efficient finite element schemes for the Shliomis model of ferrofluid flows	7
Uniform error bounds of a nested Picard iterative integrator for the Klein-Gordon-Zakharov system in the subsonic limit regime	7
A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem	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	7
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
An adaptive finite element DtN method for the acoustic-elastic interaction problem	6
A posteriori virtual element method for the acoustic vibration 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
$$\mathcal {H}_2$$ optimal rational approximation on general domains	6
Generalised Wendland functions for the sphere	6
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus	6
A hybrid boundary integral-PDE approach for the approximation of the demagnetization potential in micromagnetics	6
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	6
Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul’yev methods	6
Approximation of functions from Korobov spaces by deep convolutional neural networks	5
Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles	5
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	5
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	5
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	5
Tight frames over the quaternions and equiangular lines	5
A conforming virtual element method for Emden-Fowler model over polygonal meshes	5
Which transmission condition is the best in optimized Schwarz waveform relaxation for viscoelastic equation: Robin or characteristic?	5
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields	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

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies	5
High-order corrected trapezoidal rules for a class of singular integrals	5
Frame-normalizable sequences	5
Sparse grids vs. random points for high-dimensional polynomial approximation	5
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations	5
On a deterministic block Kaczmarz-type method and its acceleration for the solution of large-scale linear systems	5
Analysis of the geometric structure of neural networks and neural ODEs via morse functions	5
Constrained rational fitting for $$\mathcal {D}$$-stable model order reduction	5
On convergence of the generalized Lanczos trust-region method for trust-region subproblems	5
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems	5
A second-order scheme based on blended BDF for the incompressible MHD system	5
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	4
Kernel-based greedy approximation of parametric elliptic boundary value problems	4
A scaling fractional asymptotical regularization method for linear inverse problems	4
Low-rank exponential integrators for stiff differential Riccati equations	4
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform	4
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	4
Approximation of curve-based sleeve functions in high dimensions	4
GP-CMRH: an inner product free iterative method for block two-by-two nonsymmetric linear systems	4
Error analysis of a hybrid numerical method for optimal control problem governed by parabolic PDEs in random cylindrical domains	4
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	4
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	4
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	4
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	4
Multivariate rational approximation via low-rank tensors and the p-AAA algorithm	4
Spatially semi-discretely uniformly exponential stability approximation for one-dimensional thermoelastic system	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
Stabilized gradient flow schemes of phase field model for shape and topology optimization in diffusion	4
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	4
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	4
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	4
Obstructions for Gabor frames of the second-order B-spline	4
A generalized quasi-reversibility regularization method to determine a spatial source component in a time-fractional diffusion-wave equation	4
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	4
A parameterized block preconditioner for solving a class of complex symmetric linear systems	4
A direct parallel-in-time finite difference solver for quenching combustion problem	4
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology	4
Partial Floquet transformation and model order reduction of linear time-periodic systems	4
A block-randomized stochastic method with importance sampling for CP tensor decomposition	4
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	4
A mixed virtual element method for nearly incompressible linear elasticity equations	4
A stabilized trace FEM for surface Cahn–Hilliard equations: analysis and simulations	3
A primal-dual adaptive finite element method for total variation minimization	3
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	3
Exponential tractability of L2-approximation with function values	3
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	3
Numerical methods for forward fractional Feynman–Kac equation	3
Exponentially fitted methods with a local energy conservation law	3
A new approach to proper orthogonal decomposition with difference quotients	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
Symplectic QTT-FEM solution of the one-dimensional acoustic wave equation in the time domain	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
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	3
Space-time error estimates for deep neural network approximations for differential equations	3
Developing and analyzing some new finite element methods for a non-local hydrodynamic Drude model	3
A comparative numerical study of spectral properties in isogeometric collocation and Galerkin methods for acoustic waves	3
On convergence of residual-based extended Kaczmarz method for solving inconsistent linear systems	3
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	3
Data-driven optimal approximation on Hardy spaces in simply connected domains	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	3
An optimal ansatz space for moving least squares approximation on spheres	3
A sparse approximation for fractional Fourier transform	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
Curve fitting on a quantum annealer for an advanced navigation method	3
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	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
Decoupled weak Galerkin finite element method for Maxwell’s equations	3
A variable time-step IMEX BDF2 scheme for the incompressible MHD system	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	3
Nonconforming virtual element method for general second-order elliptic problems on curved domain	3
An a priori $$L^{2}$$–norm error estimate of the hybrid high-order method for a class of strongly monotone nonlinear elliptic problems	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 posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	2

Error bounds for a least squares meshless finite difference method on closed manifolds	2
New low-order mixed finite element methods for linear elasticity	2
On the asymptotically compatible energies of L1 and L1-SAV schemes for time-fractional Allen-Cahn model	2
Strong convergence of linear implicit virtual element methods for the nonlinear stochastic parabolic equation with multiplicative noise	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
A discretization theory of meshfree collocation for nonlinear systems of partial differential equations	2
An adaptive finite element DtN method for the acoustic-elastic interaction problem in periodic structures	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	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
An interpolation–regression approach for function approximation on the disk and its application to cubature formulas	2
Local behaviors of Fourier expansions for functions of limited regularities	2
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	2
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	2
Correction to: Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	2
A two-grid method with dispersion matching for finite-element Helmholtz problems	2
Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation	2
An optimal control framework for adaptive neural ODEs	2
Explicit multivariate approximations from cell-average data	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
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	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
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	2
Matching pursuit with unbounded parameter domains	2
Online identification and control of PDEs via reinforcement learning methods	2
An inertial extragradient algorithm for equilibrium and generalized split null point problems	2
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	2
A stochastic perturbation analysis of the QR decomposition and its applications	2
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	2
Robust kernel-based gradient descent with random features	2
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Efficient computation of the sinc matrix function for the integration of second-order differential equations	2
A high-order algorithm for time-domain scattering in three dimensions	2
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	2
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback controller design	2
Chebyshev accelerating technique for solving generalized non-symmetric eigenvalue problems	2
Optimal compactly supported functions in Sobolev spaces	2
Limitations of neural network training due to numerical instability of backpropagation	2
Convergence of projected subgradient method with sparse or low-rank constraints	2
Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation	2