OOIR: Observatory of International Research

Papers

(The TQCC of Numerical Methods for Partial Differential Equations is 3. 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 2022-05-01 to 2026-05-01.)

Article	Citations
	72
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	50
An Extended Virtual Element Method for the Shallow Shell Model	20
Issue Information	19
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	19
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	17
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	16
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	15
Issue Information	14
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	13
A parareal exponential integrator finite element method for semilinear parabolic equations	13
Convergence analysis of the splitting method to the nonlinear heat equation	13
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	13
A Modified Brinkman Penalization Fictitious Domain Method for the Unsteady Navier‐Stokes Equations	12
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	12
Issue Information	11
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Numerical Analysis of the Quadratic Spline Collocation Method and Averaged L1 Scheme on Graded Mesh for Nonlinear Time‐Fractional Fourth‐Order Reaction‐Diffusion Problem	11
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Issue Information	11
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	10
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	10
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	10
Jacobi Convolution Series for Petrov–Galerkin Scheme and General Fractional Calculus of Arbitrary Order Over Finite Interval	9
	9

A three‐step Oseen‐linearized finite element method for incompressible flows with damping	9
A Local RBF‐Based Differential Quadrature Method for Solving the Gray–Scott Model	9
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	9
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	8
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	8
Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	8
A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations	8
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	7
Finite Difference Method for Nonlinear Damped Viscoelastic Euler‐Bernoulli Beam Model	7
Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	7
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	7
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model	7
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The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	7
On the Stability Barrier of Hermite Type Discretizations of Advection Equations	7
Issue Information	7
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	6
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	6
A C0$$ {C}^0 $$ Finite Element Algorithm for the Sixth Order Problem With Simply Supported Boundary Conditions	6
An Adaptive Time Filter Algorithm for the 2D/3D Unsteady Triple‐Porosity Stokes Model Arising in Super‐Hydrophobic Proppant Modification in Hydraulic Fracturing Systems	6
Optimal L ² Error Quadratic Serendipity Finite Volume Element Methods for Diffusion Equations on Polygonal Meshes	6
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	6
Modeling Anomalous Diffusion With Riesz Fractional Derivatives: Applications to Pattern Formation	6
A Macro‐Bubble Enriched Divergence‐Free Finite Element on Quadrilateral Meshes	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	6
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	6
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	6
WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	6
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	6
P1$$ {P}_1 $$–Nonconforming quadrilateral finite element space with periodic boundary conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis	6
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	5
	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
A multistep collocation method for solving advection equations with delay	5
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	5
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Issue Information	5
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Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification	4
A locally calculable P³‐pressure in a decoupled method for incompressible Stokes equations	4
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	4
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	4
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	4
Inf‐Sup Stable Non‐Conforming Finite Elements on Tetrahedra With Second‐ and Third‐Order Accuracy	4

Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	4
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	4
Issue Information	4
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4
A Posteriori Error‐Driven Space‐Time Adaptive FEM for Accurate Avascular Tumor and Drug Interaction Modeling	4
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	4
The TRUNC element in any dimension and application to a modified Poisson equation	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
Issue Information	4
A flux‐based HDG method	4
Some Discontinuous Galerkin Schemes for Korteweg‐De Vries Equations: Error Estimates and Application	4
Dissipation‐Dispersion Analysis of Fully Discrete Implicit Discontinuous Galerkin Methods and Application to Stiff Hyperbolic Problems	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	3
Issue Information	3
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	3
Retraction	3
	3
A Flexible Derivation Approach for the Numerical Solution of Partial Differential Equations	3
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	3
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	3
Issue Information	3
Two‐Level Implicit High Accuracy Method in Exponential Form for 2D Quasi‐Linear Parabolic Equations on Irrational Domain	3
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Issue Information	3
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
A C⁰ interior penalty method for the phase field crystal equation	3
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3