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 2021-06-01 to 2025-06-01.)

Article	Citations
	69
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	31
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	30
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	18
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	17
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	14
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	14
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	13
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	13
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	12
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	12
Convergence analysis of the splitting method to the nonlinear heat equation	12
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	12
A parareal exponential integrator finite element method for semilinear parabolic equations	11
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	11
Issue Information	11
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	10
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	10
Issue Information	10
Analysis of sparse recovery for Legendre expansions using envelope bound	10
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	9
Issue Information	9
Issue Information	9
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	8
Numerical Analysis of the Quadratic Spline Collocation Method and Averaged L1 Scheme on Graded Mesh for Nonlinear Time‐Fractional Fourth‐Order Reaction‐Diffusion Problem	8

Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	8
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A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	8
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A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	8
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	7
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A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	7
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	7
Issue Information	7
A positivity‐preserving and energy stable scheme for a quantum diffusion equation	7
Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	7
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	7
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	7
Efficient quadrature rules for finite element discretizations of nonlocal equations	6
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	6
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	6
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	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
Issue Information	6
A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	6
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	6
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	6
A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients	6
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	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 multistep collocation method for solving advection equations with delay	6
Optimal control problem of various epidemic models with uncertainty based on deep reinforcement learning	6
Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint	6
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	6
P1$$ {P}_1 $$–Nonconforming quadrilateral finite element space with periodic boundary conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis	5
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	5
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	5
Issue Information	5
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	5
A locally calculable P³‐pressure in a decoupled method for incompressible Stokes equations	5
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	5
The TRUNC element in any dimension and application to a modified Poisson equation	5
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	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
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
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
Issue Information	4
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
A flux‐based HDG method	4
Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	4
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	4
Retraction	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	3
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	3
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
Second‐order efficient nonlinear filter stabilization for high Reynolds number flows	3
Issue Information	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
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Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	3
A C⁰ interior penalty method for the phase field crystal equation	3
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations	3
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Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations	3