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 2021-11-01 to 2025-11-01.)

Article	Citations
	71
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	39
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
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	17
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	16
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	16
An Extended Virtual Element Method for the Shallow Shell Model	15
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	13
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	13
Issue Information	13
Convergence analysis of the splitting method to the nonlinear heat equation	12
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	12
A parareal exponential integrator finite element method for semilinear parabolic equations	12
Issue Information	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
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	11
Analysis of sparse recovery for Legendre expansions using envelope bound	11
Issue Information	10
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A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	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	8

A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	8
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	8
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A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	8
Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	7
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	7
Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	7
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	7
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Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	7
A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations	7
Issue Information	7
Modeling Anomalous Diffusion With Riesz Fractional Derivatives: Applications to Pattern Formation	7
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	7
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model	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
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	6
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	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
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	6
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	6
Optimal control problem of various epidemic models with uncertainty based on deep reinforcement learning	6
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	6
A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	6
A multistep collocation method for solving advection equations with delay	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
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	6
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	5
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	5
Issue Information	5
SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification	5
WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	5
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	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
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
A C0$$ {C}^0 $$ Finite Element Algorithm for the Sixth Order Problem With Simply Supported Boundary Conditions	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	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
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	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
A flux‐based HDG method	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	4
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	4

Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	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
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	4
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	4
Issue Information	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
Issue Information	3
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	3
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
Issue Information	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
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
A C⁰ interior penalty method for the phase field crystal equation	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
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	3
Retraction	3
Some Discontinuous Galerkin Schemes for Korteweg‐De Vries Equations: Error Estimates and Application	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