OOIR: Observatory of International Research

Papers

(The TQCC of Numerical Methods for Partial Differential Equations is 2. 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 2021-04-01 to 2025-04-01.)

Article	Citations
Dual least‐squares finite element method with stabilization	68
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	28
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	26
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	23
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	17
Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in 2D	15
Issue Information	14
A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary condition	14
Convergence and optimality of an adaptive modified weak Galerkin finite element method	13
Issue Information	13
The TRUNC element in any dimension and application to a modified Poisson equation	12
Issue Information	11
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	11
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	11
	11
Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant	10
A locally calculable P³‐pressure in a decoupled method for incompressible Stokes equations	10
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	9
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	9
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	8
Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	8
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	8
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	8
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	8
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	7

Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems	7
An a priori error analysis of a type III thermoelastic problem with two porosities	7
A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation	7
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	7
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	7
Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system	7
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	6
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	6
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	6
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	6
Numerical approximations for the nonlinear time fractional reaction–diffusion equation	6
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	6
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	6
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	6
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	6
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	6
Inverse problems for discontinuous Dirac operator with eigenparameter dependent boundary and transmission conditions	6
Spectral approximation for optimal control problems governed by first bi‐harmonic equation	6
A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate	6
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number	5
Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem	5
Time filters and spurious acoustics in artificial compression methods	5
An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation	5
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	5
Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations	5
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	5
Issue Information	5
Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models	5
Issue Information	5
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	5
An adaptive mesh refinement method based on a characteristic‐compression embedded shock wave indicator for high‐speed flows	5
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	5
A kernel‐based method for solving the time‐fractional diffusion equation	5
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	5
Issue Information	4
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	4
A combined compact finite difference scheme for solving the acoustic wave equation in heterogeneous media	4
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	4
A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability	4
On the sparse multiscale representation of 2‐D Burgers equations by an efficient algorithm based on multiwavelets	4
Nitsche's method for a Robin boundary value problem in a smooth domain	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
Issue Information	3
A heat transfer problem with exponential memory and the associated thermal stresses	3
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	3
Numerical approximation of the optimal control of a population dynamics model	3

Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	3
	3
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	3
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	3
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	3
	3
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	3
Numerical analysis of a corrected Smagorinsky model	3
Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	3
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	3
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	3
A Legendre spectral‐Galerkin method for fourth‐order problems in cylindrical regions	3
Convergence analysis of the splitting method to the nonlinear heat equation	3
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	3
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	3
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	3
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	3
A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions	3
	2
On numerical study of constrained coupled shape optimization problems based on a new shape derivative method	2
	2
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	2
Retraction	2
Mixed convection of ferrofluids in a square enclosure with obstacles: Effect of iso‐perimetric shapes	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
Finite element analysis of the singularly perturbed parabolic reaction‐diffusion problems with retarded argument	2
L1‐type finite element method for time‐fractional diffusion‐wave equations on nonuniform grids	2
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	2
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	2
Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions	2
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	2
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	2
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	2
	2
Two Numerical Schemes Via an Auxiliary Function for Nonlocal Problems With Integrable Kernels	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	2
Convective thermal conditions and the thermophoretic effect's impacts on a hybrid nanofluid over a moving thin needle	2
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	2
A parareal exponential integrator finite element method for semilinear parabolic equations	2
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	2
A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis	2
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	2
Issue Information	2
A spectral collocation method for a nonlinear multidimensional Volterra integral equation	2
Issue Information	2
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	2
A minimax algorithm based on Newton's method and an application for finding multiple solutions of p‐area problems	2
Operator splitting for the fractional Korteweg‐de Vries equation	2
A class of one‐parameter alternating direction implicit methods for two‐dimensional wave equations with discrete and distributed time‐variable delays	2
A mixed element analysis of the Biot's model with Darcy–Forchheimer flow	2
A novel convenient finite difference method for shallow water waves derived by fifth‐order Kortweg and De‐Vries‐type equation	2
A flux‐based HDG method	2
An efficient flux‐variable approximation scheme for Darcy's flow	2
Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation	2
A linear finite difference scheme with error analysis designed to preserve the structure of the 2D Boussinesq paradigm equation	2
A kernel‐based pseudo‐spectral method for multi‐term and distributed order time‐fractional diffusion equations	2