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

Article	Citations
	71
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	45
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	19
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	19
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	18
An Extended Virtual Element Method for the Shallow Shell Model	17
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	16
Issue Information	15
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	14
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	14
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	13
A parareal exponential integrator finite element method for semilinear parabolic equations	13
Issue Information	12
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	12
Convergence analysis of the splitting method to the nonlinear heat equation	12
	11
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
	11
Analysis of sparse recovery for Legendre expansions using envelope bound	11
	11
Issue Information	11
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	9
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	9
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	9
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	9

A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	9
	8
Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	8
A Local RBF‐Based Differential Quadrature Method for Solving the Gray–Scott Model	8
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	8
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	8
Jacobi Convolution Series for Petrov–Galerkin Scheme and General Fractional Calculus of Arbitrary Order Over Finite Interval	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	7
	7
Modeling Anomalous Diffusion With Riesz Fractional Derivatives: Applications to Pattern Formation	7
Issue Information	7
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model	7
Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	7
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	7
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
On the Stability Barrier of Hermite Type Discretizations of Advection Equations	7
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	7
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	7
Optimal control problem of various epidemic models with uncertainty based on deep reinforcement learning	6
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	6
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	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
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	6
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	6
WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	6
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	6
A multistep collocation method for solving advection equations with delay	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
A locally calculable P³‐pressure in a decoupled method for incompressible Stokes equations	5
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	5
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	5
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	5
The TRUNC element in any dimension and application to a modified Poisson equation	5
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	5
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	5
Issue Information	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	4
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	4
Some Discontinuous Galerkin Schemes for Korteweg‐De Vries Equations: Error Estimates and Application	4
Inf‐Sup Stable Non‐Conforming Finite Elements on Tetrahedra With Second‐ and Third‐Order Accuracy	4

A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema	4
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	4
A flux‐based HDG method	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	4
Issue Information	4
SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification	4
	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
Issue Information	4
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	4
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	3
Dissipation‐Dispersion Analysis of Fully Discrete Implicit Discontinuous Galerkin Methods and Application to Stiff Hyperbolic Problems	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
	3
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	3
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	3
Retraction	3
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	3
Issue Information	3
Issue Information	3
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
Two‐Level Implicit High Accuracy Method in Exponential Form for 2D Quasi‐Linear Parabolic Equations on Irrational Domain	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	3
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	3
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	3
A C⁰ interior penalty method for the phase field crystal equation	3
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	3
Issue Information	3
Deriving Locally Conservative Fluxes From High‐Order Finite Element Solutions by Solving a Constrained Minimization Problem	3
A Flexible Derivation Approach for the Numerical Solution of Partial Differential Equations	3
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	3