Numerical Methods for Partial Differential Equations

Article	Citations
	71
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	45
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	19
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	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
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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	11
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Analysis of sparse recovery for Legendre expansions using envelope bound	11
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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
Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	8
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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
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	7
A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations	7
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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
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
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
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
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
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A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
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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
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
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
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
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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
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A C0 interior penalty method for the phase field crystal equation	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
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	2
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Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
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A systematic study on weak Galerkin finite element method for second‐order parabolic problems	2
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	2
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	2
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	2
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	2
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	2
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	2
Issue Information	2
Unfitted mixed finite element methods for elliptic interface problems	2
Numerical solution of convected wave equation in free field using artificial boundary method	2
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	2
Dual least‐squares finite element method with stabilization	2
A heat transfer problem with exponential memory and the associated thermal stresses	2
A note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	2
Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	2
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
A priori error estimates of two monolithic schemes for Biot's consolidation model	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	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 new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	2
A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	2
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	2
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	2
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Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	2
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
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Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	2

An a priori error analysis of a type III thermoelastic problem with two porosities	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves	2
Numerical Method and Analysis for the Coupled Sine‐Gordon Equations on Unbounded Domains	2
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
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
Nitsche's method for a Robin boundary value problem in a smooth domain	1
A numerical scheme for the optimal control of groundwater pollution	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
A Linearly Implicit and Structure‐Preserving Scheme for the Ginzburg–Landau–Schrödinger Equation	1
Primal‐dual active set algorithm for valuating American options under regime switching	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	1
Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density	1
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	1
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	1
Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	1
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	1
Fast ADI Finite Difference Method for Two‐Dimensional Space‐Fractional Diffusion Equations on Nonuniform Spatial Grids	1
A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model	1
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms	1
A well‐balanced and entropy stable scheme for a reduced blood flow model	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1
Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation	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
Two Methods for Solving the Two‐Dimensional Black–Scholes Equation	1
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1
Controllability of nonlinear Hilfer fractional Langevin dynamical system	1
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	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
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	1
Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids	1
A Priori Error Estimates for H(curl)$$ \mathbf{H}\left(\operatorname{curl}\right) $$ and H(div)$$ \mathbf{H}\left(\operatorname{div}\right) $$‐Elliptic Interface Problems: Least‐Squares Weak Galerkin	1
Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization	1
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	1
A kernel‐based method for solving the time‐fractional diffusion equation	1
Structure‐Preserving Approximation of the Cahn‐Hilliard‐Biot System	1
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	1
A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis	1
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions	1
Mixed Shifted Generalized Laguerre–Fourier Spectral Method for Exterior Problem of Fisher Equation	1
An efficient flux‐variable approximation scheme for Darcy's flow	1
On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation	1
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	1
On the optimality of voronoi‐based column selection	1
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation	1
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	1
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	1
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	1
Three dimensional high order finite volume element schemes for elliptic equations	1
A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations	1
Issue Information	1
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods	1
Maximum Convergence of a Novel High‐Precision Conservative Compact Difference Scheme for the Coupled Nonlinear Schrödinger (CNLS) Equations	1
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	1
A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations	1
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	1
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	1
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	1
A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	1
On the SAV‐DG method for a class of fourth order gradient flows	1
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A new ϕ‐FEM approach for problems with natural boundary conditions	1
Numerical analysis of a corrected Smagorinsky model	1
Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
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