Numerical Methods for Partial Differential Equations

Article	Citations
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	69
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	28
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	26
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	17
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The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	14
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	13
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	13
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	12
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	11
A parareal exponential integrator finite element method for semilinear parabolic equations	11
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Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	11
Convergence analysis of the splitting method to the nonlinear heat equation	11
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	10
Analysis of sparse recovery for Legendre expansions using envelope bound	9
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	9
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	8
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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	8
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A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	8

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A three‐step Oseen‐linearized finite element method for incompressible flows with damping	7
Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	7
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	7
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	7
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	7
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Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	7
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	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
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	6
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	6
A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients	6
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	6
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	6
A positivity‐preserving and energy stable scheme for a quantum diffusion equation	6
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Efficient quadrature rules for finite element discretizations of nonlocal equations	6
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	6
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Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	6
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	6
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	5
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A multistep collocation method for solving advection equations with delay	5
A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
An Adaptive Time Filter Algorithm for the 2D/3D Unsteady Triple‐Porosity Stokes Model Arising in Super‐Hydrophobic Proppant Modification in Hydraulic Fracturing Systems	5
Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	5
Optimal control problem of various epidemic models with uncertainty based on deep reinforcement learning	5
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P1$$ {P}_1 $$–Nonconforming quadrilateral finite element space with periodic boundary conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis	5
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	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
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	5
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	4
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A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	4
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	4
The TRUNC element in any dimension and application to a modified Poisson equation	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
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	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
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	3

Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	3
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	3
A flux‐based HDG method	3
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	3
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	3
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	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
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	3
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	3
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	3
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
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Retraction	3
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	2
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	2
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	2
Second‐order efficient nonlinear filter stabilization for high Reynolds number flows	2
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves	2
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	2
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Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	2
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Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	2
A C0 interior penalty method for the phase field crystal equation	2
Numerical approximations of chromatographic models	2
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	2
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
Stability and error analysis of a splitting method using Robin–Robin coupling applied to a fluid–structure interaction problem	2
Dual least‐squares finite element method with stabilization	2
A priori error estimates of two monolithic schemes for Biot's consolidation model	2
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	2
Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem	2
Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations	2
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	2
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	2
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
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A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	2
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	2
A heat transfer problem with exponential memory and the associated thermal stresses	2
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Error analysis of a fully discrete projection method for magnetohydrodynamic system	2
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	2
Unfitted mixed finite element methods for elliptic interface problems	2
An a priori error analysis of a type III thermoelastic problem with two porosities	2
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	2
A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	2
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
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A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	2
Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators	2
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	2
On the compact difference scheme for the two‐dimensional coupled nonlinear Schrödinger equations	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	2
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations	2
A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1
Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids	1
A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary condition	1
A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations	1
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	1
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	1
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1
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Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation	1

On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation	1
A note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	1
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation	1
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	1
Numerical solution of convected wave equation in free field using artificial boundary method	1
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	1
A kernel‐based method for solving the time‐fractional diffusion equation	1
A well‐balanced and entropy stable scheme for a reduced blood flow model	1
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	1
On the SAV‐DG method for a class of fourth order gradient flows	1
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	1
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	1
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	1
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	1
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	1
A new ϕ‐FEM approach for problems with natural boundary conditions	1
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	1
Novel superconvergence analysis of anisotropic triangular FEM for a multi‐term time‐fractional mixed sub‐diffusion and diffusion‐wave equation with variable coefficients	1
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	1
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion	1
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	1
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	1
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	1
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	1
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system	1
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	1
Semi‐analytic time differencing methods for singularly perturbed initial value problems	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	1
Numerical approximation of solutions of the equations of quasistatic electroporoelasticity	1
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On the optimality of voronoi‐based column selection	1
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	1
Collocation method for one dimensional nonlocal diffusion equations	1
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	1
Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon	1
Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	1
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Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters	1
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