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 2020-03-01 to 2024-03-01.)

Article	Citations
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation	38
Drift-preserving numerical integrators for stochastic Hamiltonian systems	30
Simple maximum principle preserving time-stepping methods for time-fractional Allen-Cahn equation	26
Optimal H1 spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation	22
The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers’ equation	22
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs	17
A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation	17
Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation	16
Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method	16
The role of mesh quality and mesh quality indicators in the virtual element method	16
Persistence Curves: A canonical framework for summarizing persistence diagrams	16
Virtual element methods for the three-field formulation of time-dependent linear poroelasticity	16
Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model	15
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	15
Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations	14
Multigrid preconditioners for anisotropic space-fractional diffusion equations	13
p- and hp- virtual elements for the Stokes problem	13
A unified analysis of a class of quadratic finite volume element schemes on triangular meshes	12
High-order cut finite elements for the elastic wave equation	12
Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators	11
Analysis of adaptive synchrosqueezing transform with a time-varying parameter	11
A family of C1 quadrilateral finite elements	11
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method	11
A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations	10
A stable second-order BDF scheme for the three-dimensional Cahn–Hilliard–Hele–Shaw system	9

Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	9
A mixed virtual element method for the vibration problem of clamped Kirchhoff plate	9
Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation	9
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	8
A rational RBF interpolation with conditionally positive definite kernels	8
Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations	8
An integral equation–based numerical method for the forced heat equation on complex domains	8
Space-time error estimates for deep neural network approximations for differential equations	8
Joint spectral radius and ternary hermite subdivision	8
Learning via variably scaled kernels	8
A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction	8
A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model	8
Mixed precision path tracking for polynomial homotopy continuation	7
Accelerated hybrid methods for solving pseudomonotone equilibrium problems	7
Structure-preserving interpolation of bilinear control systems	7
Trefftz discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport	7
Tensor completion via bilevel minimization with fixed-point constraint to estimate missing elements in noisy data	7
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	7
Rigorous and effective a-posteriori error bounds for nonlinear problems—application to RB methods	7
Generalized Born-Jordan distributions and applications	7
An adaptive spectral graph wavelet method for PDEs on networks	7
Solving partial differential equations on (evolving) surfaces with radial basis functions	7
Data-driven uncertainty quantification in macroscopic traffic flow models	7
A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation	6
Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems	6
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	6
New convergence analysis of a primal-dual algorithm with large stepsizes	6
Virtual element methods for nonlocal parabolic problems on general type of meshes	6
Least-Squares Padé approximation of parametric and stochastic Helmholtz maps	6
A conservative sine pseudo-spectral-difference method for multi-dimensional coupled Gross–Pitaevskii equations	6
Adaptive hybridizable discontinuous Galerkin methods for nonstationary convection diffusion problems	6
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	6
Kernel aggregated fast multipole method	6
Frames and weak frames for unbounded operators	6
Hankel-norm approximation of large-scale descriptor systems	6
The hot spots conjecture can be false: some numerical examples	5
Numerical algorithms for water waves with background flow over obstacles and topography	5
Exponential mean-square stability properties of stochastic linear multistep methods	5
A quadratic finite volume method for nonlinear elliptic problems	5
Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering	5
A structure-preserving algorithm for surface water flows with transport processes	5
Fast randomized matrix and tensor interpolative decomposition using CountSketch	5
A characterization of supersmoothness of multivariate splines	5
Randomized linear algebra for model reduction—part II: minimal residual methods and dictionary-based approximation	5
An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations	5
Balanced truncation of linear time-invariant systems over finite-frequency ranges	5
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	4
Edge detection with trigonometric polynomial shearlets	4
Computing the reciprocal of a ϕ-function by rational approximation	4
Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements	4

Comparison of integral equations for the Maxwell transmission problem with general permittivities	4
Difference potentials method for models with dynamic boundary conditions and bulk-surface problems	4
Symplectic geometry and connectivity of spaces of frames	4
Worst-case optimal approximation with increasingly flat Gaussian kernels	4
Tensor rank bounds for point singularities in ℝ3	4
Determination of temperature distribution and thermal flux for two-dimensional inhomogeneous sideways heat equations	4
Counting the dimension of splines of mixed smoothness	4
Structured backward error analysis for generalized saddle point problems	4
Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations	4
The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers	4
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	4
Unified construction and L2 analysis for the finite volume element method over tensorial meshes	4
Accurate singular values of a class of parameterized negative matrices	4
Continuous window functions for NFFT	4
A generalisation of de la Vallée-Poussin procedure to multivariate approximations	4
A hybrid collocation-perturbation approach for PDEs with random domains	4
High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation	4
A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampère equation	4
Unconditionally optimal convergence analysis of second-order BDF Galerkin finite element scheme for a hybrid MHD system	4
Clothoid fitting and geometric Hermite subdivision	4
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations	4
Cs-smooth isogeometric spline spaces over planar bilinear multi-patch parameterizations	4
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels	4
Stabilization of spline bases by extension	4
Characterization and extensive study of cubic and quintic algebraic trigonometric planar PH curves	4
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	4
An hp-version of the C0-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems	4