OOIR: Observatory of International Research

Papers

(The TQCC of Advances in Computational Mathematics is 4. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-11-01 to 2024-11-01.)

Article	Citations
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	41
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	29
The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers’ equation	28
The role of mesh quality and mesh quality indicators in the virtual element method	22
A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation	22
Persistence Curves: A canonical framework for summarizing persistence diagrams	20
Virtual element methods for the three-field formulation of time-dependent linear poroelasticity	19
Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations	19
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs	19
Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation	16
p- and hp- virtual elements for the Stokes problem	16
A family of C1 quadrilateral finite elements	15
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method	15
Structure-preserving interpolation of bilinear control systems	13
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	12
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	11
A rational RBF interpolation with conditionally positive definite kernels	11
Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators	11
A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations	10
Space-time error estimates for deep neural network approximations for differential equations	10
A stable second-order BDF scheme for the three-dimensional Cahn–Hilliard–Hele–Shaw system	10
Randomized linear algebra for model reduction—part II: minimal residual methods and dictionary-based approximation	10
Tensor completion via bilevel minimization with fixed-point constraint to estimate missing elements in noisy data	9
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	9
A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation	9

Learning via variably scaled kernels	8
A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model	8
Data-driven uncertainty quantification in macroscopic traffic flow models	8
Kernel aggregated fast multipole method	8
Mixed precision path tracking for polynomial homotopy continuation	8
Joint spectral radius and ternary hermite subdivision	8
Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations	7
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	7
New convergence analysis of a primal-dual algorithm with large stepsizes	7
A Grassmann manifold handbook: basic geometry and computational aspects	7
Balanced truncation of linear time-invariant systems over finite-frequency ranges	7
An adaptive discontinuous finite volume element method for the Allen-Cahn equation	7
The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers	7
An adaptive spectral graph wavelet method for PDEs on networks	7
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	7
A stabilizer-free pressure-robust finite element method for the Stokes equations	6
Accurate computations with matrices related to bases {tieλt}	6
Approximation of functions from Korobov spaces by deep convolutional neural networks	6
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	6
Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems	6
Small errors imply large evaluation instabilities	6
A hybrid collocation-perturbation approach for PDEs with random domains	6
Exponential mean-square stability properties of stochastic linear multistep methods	6
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations	6
A quadratic finite volume method for nonlinear elliptic problems	6
On basis constructions in finite element exterior calculus	6
State-dependent Riccati equation feedback stabilization for nonlinear PDEs	5
Numerical algorithms for water waves with background flow over obstacles and topography	5
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	5
An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations	5
Clothoid fitting and geometric Hermite subdivision	5
Accurate singular values of a class of parameterized negative matrices	5
Symplectic geometry and connectivity of spaces of frames	5
Continuous window functions for NFFT	5
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations	5
A structure-preserving algorithm for surface water flows with transport processes	5
A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampère equation	5
Unified construction and L2 analysis for the finite volume element method over tensorial meshes	5
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	5
Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering	5
Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds	5
High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation	5
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects	5
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	5
Stabilization of spline bases by extension	5
Comparison of integral equations for the Maxwell transmission problem with general permittivities	4
Cs-smooth isogeometric spline spaces over planar bilinear multi-patch parameterizations	4
A fast and oblivious matrix compression algorithm for Volterra integral operators	4
Limited memory restarted ℓp-ℓq minimization methods using generalized Krylov subspaces	4
Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements	4

A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law	4
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	4
The hot spots conjecture can be false: some numerical examples	4
Counting the dimension of splines of mixed smoothness	4
A generalisation of de la Vallée-Poussin procedure to multivariate approximations	4
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	4
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	4
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	4
Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials	4
A fast time domain solver for the equilibrium Dyson equation	4
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	4
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	4
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	4
Tensor rank bounds for point singularities in ℝ3	4
Rapid evaluation of the spectral signal detection threshold and Stieltjes transform	4
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels	4
Edge detection with trigonometric polynomial shearlets	4
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	4
Computing the reciprocal of a ϕ-function by rational approximation	4
An hp-version Legendre spectral collocation method for multi-order fractional differential equations	4
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	4
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	4
Adaptive and optimal pointwise deconvolution density estimations by wavelets	4
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	4
A new framework for polynomial approximation to differential equations	4