Numerical Methods for Partial Differential Equations

Article	Citations
	72
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	50
An Extended Virtual Element Method for the Shallow Shell Model	20
Issue Information	19
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	19
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	17
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	16
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	15
Issue Information	14
A parareal exponential integrator finite element method for semilinear parabolic equations	13
Convergence analysis of the splitting method to the nonlinear heat equation	13
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
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	12
A Modified Brinkman Penalization Fictitious Domain Method for the Unsteady Navier‐Stokes Equations	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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Issue Information	11
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A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	10
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	10
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	10
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	9
A Local RBF‐Based Differential Quadrature Method for Solving the Gray–Scott Model	9

A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	9
Jacobi Convolution Series for Petrov–Galerkin Scheme and General Fractional Calculus of Arbitrary Order Over Finite Interval	9
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An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	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	8
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	8
Finite Difference Method for Nonlinear Damped Viscoelastic Euler‐Bernoulli Beam Model	7
Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	7
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	7
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model	7
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The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	7
On the Stability Barrier of Hermite Type Discretizations of Advection Equations	7
Issue Information	7
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	7
Optimal L 2 Error Quadratic Serendipity Finite Volume Element Methods for Diffusion Equations on Polygonal Meshes	6
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	6
Modeling Anomalous Diffusion With Riesz Fractional Derivatives: Applications to Pattern Formation	6
A Macro‐Bubble Enriched Divergence‐Free Finite Element on Quadrilateral Meshes	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
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	6
WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	6
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	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
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	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
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
A multistep collocation method for solving advection equations with delay	5
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	5
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Issue Information	5
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Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	5
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Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	4
Inf‐Sup Stable Non‐Conforming Finite Elements on Tetrahedra With Second‐ and Third‐Order Accuracy	4
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	4
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	4
Issue Information	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4

Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	4
A Posteriori Error‐Driven Space‐Time Adaptive FEM for Accurate Avascular Tumor and Drug Interaction Modeling	4
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	4
The TRUNC element in any dimension and application to a modified Poisson equation	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
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Some Discontinuous Galerkin Schemes for Korteweg‐De Vries Equations: Error Estimates and Application	4
Dissipation‐Dispersion Analysis of Fully Discrete Implicit Discontinuous Galerkin Methods and Application to Stiff Hyperbolic Problems	4
A flux‐based HDG method	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification	4
A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations	4
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	4
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	4
A Flexible Derivation Approach for the Numerical Solution of Partial Differential Equations	3
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	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
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Issue Information	3
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
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
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	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
Retraction	3
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Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	2
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	2
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	2
Issue Information	2
Error analysis of a fully discrete projection method for magnetohydrodynamic system	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	2
Deriving Locally Conservative Fluxes From High‐Order Finite Element Solutions by Solving a Constrained Minimization Problem	2
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	2
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	2
A priori error estimates of two monolithic schemes for Biot's consolidation model	2
Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	2
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	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
Unfitted mixed finite element methods for elliptic interface problems	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	2
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	2
Numerical solution of convected wave equation in free field using artificial boundary method	2
A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	2
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	2
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	2
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	2
Pseudostress‐Based Velocity Formulation for the Stokes‐Brinkman‐Type Eigenvalue Problem: A Priori and a Posteriori Error Analysis	2
A Multi‐Domain Space‐Time Spectral Collocation Method for the Huxley Equation	2
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Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	2
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	2
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
Improved Error Estimates on Time‐Splitting Method for the Space Fractional Klein–Gordon–Schrödinger Equation With the Small Coupling Constant	2
Issue Information	2
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An a priori error analysis of a type III thermoelastic problem with two porosities	2
The Landau–Lifshitz–Bloch Equation With Spin Diffusion: Global Strong Solution and Finite Element Approximation	2
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	2
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	2
Dual least‐squares finite element method with stabilization	2
Issue Information	1
A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	1
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	1
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	1
On the optimality of voronoi‐based column selection	1
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
Mixed Finite Element Methods for the Nonlinear Stochastic Elastodynamics Equations With Multiplicative Noise	1
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	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
A Linearly Implicit and Structure‐Preserving Scheme for the Ginzburg–Landau–Schrödinger Equation	1
Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density	1
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	1
Two Methods for Solving the Two‐Dimensional Black–Scholes Equation	1
Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization	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
On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation	1
Controllability of nonlinear Hilfer fractional Langevin dynamical system	1
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	1
On the Stabilizer‐Free Immersed Weak Galerkin FEM: A Posteriori Error Estimation in a Non‐Conforming Framework	1
Towards hybrid two‐phase modelling using linear domain decomposition	1
A Hybrid WENO Method for Hyperbolic Conservation Laws on the Polygonal Mesh With Mixed Elements	1
Unconditional H2$$ {H}^2 $$‐stability of the Euler implicit/explicit SAV‐based scheme for the 2D Navier–Stokes equations with smooth or nonsmooth initial data	1
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A numerical scheme for the optimal control of groundwater pollution	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
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
Issue Information	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1
An efficient flux‐variable approximation scheme for Darcy's flow	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
Structure‐Preserving Approximation of the Cahn‐Hilliard‐Biot System	1
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	1
Jacobi‐Galerkin Spectral Method for the Fractional Diffusion Equation	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	1
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	1
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	1
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	1
Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods	1
A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model	1
Fast ADI Finite Difference Method for Two‐Dimensional Space‐Fractional Diffusion Equations on Nonuniform Spatial Grids	1
Linearized compact difference schemes applied to nonlinear variable coefficient parabolic equations with distributed delay	1
Numerical analysis of a corrected Smagorinsky model	1
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Adaptive finite element methods for scalar double‐well problem	1
Mixed Shifted Generalized Laguerre–Fourier Spectral Method for Exterior Problem of Fisher Equation	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
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	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
Superconvergent Meshless Collocation Method for Nonlinear Neutral Delay‐Reaction‐Diffusion Equation	1
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	1
Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation	1
Three dimensional high order finite volume element schemes for elliptic equations	1
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation	1
A kernel‐based method for solving the time‐fractional diffusion equation	1
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	1
Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	1
Maximum Convergence of a Novel High‐Precision Conservative Compact Difference Scheme for the Coupled Nonlinear Schrödinger (CNLS) Equations	1
A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations	1
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions	1
Nitsche's method for a Robin boundary value problem in a smooth domain	1
Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
Primal‐dual active set algorithm for valuating American options under regime switching	1
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	1
Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids	1
An error analysis of the finite element method of the Stokes equations with parameter based on the singular function expansion	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
Issue Information	1
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	1
A note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	1