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 2022-08-01 to 2026-08-01.)

Article	Citations
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	73
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	52
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	21
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	20
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	20
An Extended Virtual Element Method for the Shallow Shell Model	19
Issue Information	16
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	15
Issue Information	15
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	14
Convergence analysis of the splitting method to the nonlinear heat equation	14
A Linearized Conservative Compact Difference Scheme for the BBM–Burgers Equation With Numerical Simulations	13
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A Modified Brinkman Penalization Fictitious Domain Method for the Unsteady Navier‐Stokes Equations	13
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	13
A parareal exponential integrator finite element method for semilinear parabolic equations	13
Numerical Analysis of the Quadratic Spline Collocation Method and Averaged L1 Scheme on Graded Mesh for Nonlinear Time‐Fractional Fourth‐Order Reaction‐Diffusion Problem	13
Jacobi Convolution Series for Petrov–Galerkin Scheme and General Fractional Calculus of Arbitrary Order Over Finite Interval	12
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A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	11
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	11
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	11
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	10
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	10
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A Local RBF‐Based Differential Quadrature Method for Solving the Gray–Scott Model	10
On the Stability Barrier of Hermite Type Discretizations of Advection Equations	9
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	9
Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	9
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	9
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Finite Difference Method for Nonlinear Damped Viscoelastic Euler‐Bernoulli Beam Model	8
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	8
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model	8
Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	8
Issue Information	8
A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations	8
Optimal L ² Error Quadratic Serendipity Finite Volume Element Methods for Diffusion Equations on Polygonal Meshes	7
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	7
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	7
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	7
Modeling Anomalous Diffusion With Riesz Fractional Derivatives: Applications to Pattern Formation	7
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	7
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	7
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	7
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WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	6
A C0$$ {C}^0 $$ Finite Element Algorithm for the Sixth Order Problem With Simply Supported Boundary Conditions	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	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
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	6
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	6
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	6
A Spectral Galerkin Approximation for Second‐Order Non‐Selfadjoint Steklov Eigenvalue Problems in Complex Domains	6
A Macro‐Bubble Enriched Divergence‐Free Finite Element on Quadrilateral Meshes	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
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	6
A multistep collocation method for solving advection equations with delay	6
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A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
The TRUNC element in any dimension and application to a modified Poisson equation	5
Inf‐Sup Stable Non‐Conforming Finite Elements on Tetrahedra With Second‐ and Third‐Order Accuracy	5
A flux‐based HDG method	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
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Issue Information	5
A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema	5
Issue Information	5
SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification	5
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
A locally calculable P³‐pressure in a decoupled method for incompressible Stokes equations	5
A Numerical Approach for (2+1)D Saturable Nonlinear Schrödinger Equations With Generalized Loss	5
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	5

Issue Information	4
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	4
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	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 discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	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
An Efficient Probabilistic Scheme for the Exit Time Probability of α‐Stable Lévy Process	4
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	4
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	4
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	4
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	4
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
Issue Information	3
Deriving Locally Conservative Fluxes From High‐Order Finite Element Solutions by Solving a Constrained Minimization Problem	3
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	3
Unfitted mixed finite element methods for elliptic interface problems	3
Issue Information	3
A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	3
Retraction	3
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
Issue Information	3
A Flexible Derivation Approach for the Numerical Solution of Partial Differential Equations	3
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Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	3
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	3
Error analysis of a fully discrete projection method for magnetohydrodynamic system	3
Regularization Methods Based on a Priori Information for Backward Inhomogeneous Caputo Time‐Fractional Parabolic Equation	3
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Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	3
Issue Information	3
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	3
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	3
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	3
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	3
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves	3
A C⁰ interior penalty method for the phase field crystal equation	3
Two‐Level Implicit High Accuracy Method in Exponential Form for 2D Quasi‐Linear Parabolic Equations on Irrational Domain	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3