Numerical Methods for Partial Differential Equations

Article	Citations
	71
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	33
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	18
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	16
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	16
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	16
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	15
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	14
Convergence analysis of the splitting method to the nonlinear heat equation	13
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	13
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Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	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	12
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	11
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Analysis of sparse recovery for Legendre expansions using envelope bound	11
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A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	10
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A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	9
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Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	9
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	9

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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	9
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	8
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	8
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	8
Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	8
Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	7
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The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	7
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	7
A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations	7
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	7
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	7
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Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	7
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	7
A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients	7
Efficient quadrature rules for finite element discretizations of nonlocal equations	6
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	6
Optimal control problem of various epidemic models with uncertainty based on deep reinforcement learning	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
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	6
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	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
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	6
A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	6
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	6
Issue Information	6
A multistep collocation method for solving advection equations with delay	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	6
Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint	6
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	5
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Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	5
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	5
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations	5
WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	5
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
The TRUNC element in any dimension and application to a modified Poisson equation	5
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	5
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	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
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	4
Some Discontinuous Galerkin Schemes for Korteweg‐De Vries Equations: Error Estimates and Application	4
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	4
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	4

Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	4
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	4
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A flux‐based HDG method	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	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 posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
Retraction	3
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	3
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Second‐order efficient nonlinear filter stabilization for high Reynolds number flows	3
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	3
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	3
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
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Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
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
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A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	2
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	2
Unfitted mixed finite element methods for elliptic interface problems	2
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves	2
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	2
Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	2
Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	2
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	2
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Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	2
An a priori error analysis of a type III thermoelastic problem with two porosities	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
Dual least‐squares finite element method with stabilization	2
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
Error analysis of a fully discrete projection method for magnetohydrodynamic system	2
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
Stability and error analysis of a splitting method using Robin–Robin coupling applied to a fluid–structure interaction problem	2
Issue Information	2
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	2
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	2
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	2
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	2
Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	2
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	2
A priori error estimates of two monolithic schemes for Biot's consolidation model	2
A heat transfer problem with exponential memory and the associated thermal stresses	2
On the compact difference scheme for the two‐dimensional coupled nonlinear Schrödinger equations	2
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	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
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	2
Numerical Method and Analysis for the Coupled Sine‐Gordon Equations on Unbounded Domains	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
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	2
Numerical solution of convected wave equation in free field using artificial boundary method	2
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
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
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	1
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	1

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A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	1
Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon	1
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	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
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
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	1
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1
Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation	1
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion	1
Semi‐analytic time differencing methods for singularly perturbed initial value problems	1
Maximum Convergence of a Novel High‐Precision Conservative Compact Difference Scheme for the Coupled Nonlinear Schrödinger (CNLS) Equations	1
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An efficient flux‐variable approximation scheme for Darcy's flow	1
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	1
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	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
A well‐balanced and entropy stable scheme for a reduced blood flow model	1
Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
Numerical approximation of solutions of the equations of quasistatic electroporoelasticity	1
A new ϕ‐FEM approach for problems with natural boundary conditions	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations	1
On the optimality of voronoi‐based column selection	1
Numerical analysis of a corrected Smagorinsky model	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
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Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
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Mixed Shifted Generalized Laguerre–Fourier Spectral Method for Exterior Problem of Fisher Equation	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 note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	1
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	1
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	1
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms	1
Nitsche's method for a Robin boundary value problem in a smooth domain	1
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	1
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	1
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	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
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	1
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Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	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
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
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	1
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	1
On the SAV‐DG method for a class of fourth order gradient flows	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