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	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
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	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
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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
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	2
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	2
A priori error estimates of two monolithic schemes for Biot's consolidation model	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	2
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	2
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	2
Dual least‐squares finite element method with stabilization	2
A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	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
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	2
Deriving Locally Conservative Fluxes From High‐Order Finite Element Solutions by Solving a Constrained Minimization Problem	2
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	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 generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	2
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	2
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
Issue Information	2
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	2
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	2
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
Unfitted mixed finite element methods for elliptic interface problems	2
Error analysis of a fully discrete projection method for magnetohydrodynamic system	2
Second‐order efficient nonlinear filter stabilization for high Reynolds number flows	2
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
A heat transfer problem with exponential memory and the associated thermal stresses	2
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Numerical solution of convected wave equation in free field using artificial boundary method	2
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	2
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
Numerical Method and Analysis for the Coupled Sine‐Gordon Equations on Unbounded Domains	2
On the compact difference scheme for the two‐dimensional coupled nonlinear Schrödinger equations	2
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	2
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
An a priori error analysis of a type III thermoelastic problem with two porosities	2
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	2
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	2
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Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	2
Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	2
Issue Information	1
A well‐balanced and entropy stable scheme for a reduced blood flow model	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
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1

Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	1
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	1
Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods	1
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	1
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms	1
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	1
Numerical approximation of solutions of the equations of quasistatic electroporoelasticity	1
Maximum Convergence of a Novel High‐Precision Conservative Compact Difference Scheme for the Coupled Nonlinear Schrödinger (CNLS) Equations	1
Issue Information	1
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	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
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	1
A new ϕ‐FEM approach for problems with natural boundary conditions	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	1
A Linearly Implicit and Structure‐Preserving Scheme for the Ginzburg–Landau–Schrödinger Equation	1
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
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Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	1
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A note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	1
Mixed Shifted Generalized Laguerre–Fourier Spectral Method for Exterior Problem of Fisher Equation	1
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	1
A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	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
Numerical analysis of a corrected Smagorinsky model	1
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	1
Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids	1
A numerical scheme for the optimal control of groundwater pollution	1
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	1
Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters	1
Issue Information	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
A kernel‐based method for solving the time‐fractional diffusion equation	1
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion 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
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	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
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	1
On the SAV‐DG method for a class of fourth order gradient flows	1
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	1
Nitsche's method for a Robin boundary value problem in a smooth domain	1
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	1
An efficient flux‐variable approximation scheme for Darcy's flow	1
A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations	1
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	1
On the optimality of voronoi‐based column selection	1
Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
Issue Information	1
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	1
Three dimensional high order finite volume element schemes for elliptic equations	1
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	1
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	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
A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations	1
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	1
Two Methods for Solving the Two‐Dimensional Black–Scholes Equation	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1