Numerical Methods for Partial Differential Equations

Article	Citations
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	65
Dual least‐squares finite element method with stabilization	28
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	26
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	17
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	17
Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in 2D	14
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	14
Issue Information	12
Convergence and optimality of an adaptive modified weak Galerkin finite element method	11
Issue Information	11
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	11
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	10
	10
A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations	9
Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant	9
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	8
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	8
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	8
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	8
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	8
Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	8
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	7
A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation	7
Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems	7
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	7

Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system	7
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	7
Inverse problems for discontinuous Dirac operator with eigenparameter dependent boundary and transmission conditions	6
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	6
Numerical approximations for the nonlinear time fractional reaction–diffusion equation	6
Time filters and spurious acoustics in artificial compression methods	6
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	6
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	6
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	6
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	6
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	6
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	6
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	5
A kernel‐based method for solving the time‐fractional diffusion equation	5
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	5
Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number	5
Spectral approximation for optimal control problems governed by first bi‐harmonic equation	5
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	5
The TRUNC element in any dimension and application to a modified Poisson equation	5
	5
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	5
Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models	5
Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem	5
An adaptive mesh refinement method based on a characteristic‐compression embedded shock wave indicator for high‐speed flows	5
Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations	5
An a priori error analysis of a type III thermoelastic problem with two porosities	5
A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	4
An efficient flux‐variable approximation scheme for Darcy's flow	4
Issue Information	4
L1‐type finite element method for time‐fractional diffusion‐wave equations on nonuniform grids	4
A flux‐based HDG method	4
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	4
Issue Information	4
A parareal exponential integrator finite element method for semilinear parabolic equations	4
A linear finite difference scheme with error analysis designed to preserve the structure of the 2D Boussinesq paradigm equation	4
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	3
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	3
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	3
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	3
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	3
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	3
Numerical approximation of the optimal control of a population dynamics model	3
An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation	3
A Legendre spectral‐Galerkin method for fourth‐order problems in cylindrical regions	3
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	3
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	3

A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	3
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	3
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	3
A combined compact finite difference scheme for solving the acoustic wave equation in heterogeneous media	3
Numerical analysis of a corrected Smagorinsky model	3
A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability	3
A heat transfer problem with exponential memory and the associated thermal stresses	3
Higher‐order explicit schemes based on the method of characteristics for hyperbolic equations with crossing straight‐line characteristics	3
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	3
A novel convenient finite difference method for shallow water waves derived by fifth‐order Kortweg and De‐Vries‐type equation	3
Issue Information	3
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	3
Nitsche's method for a Robin boundary value problem in a smooth domain	3
Operator splitting for the fractional Korteweg‐de Vries equation	2
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	2
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	2
	2
Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	2
A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems	2
On the sparse multiscale representation of 2‐D Burgers equations by an efficient algorithm based on multiwavelets	2
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	2
A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis	2
Two Numerical Schemes Via an Auxiliary Function for Nonlocal Problems With Integrable Kernels	2
A mixed element analysis of the Biot's model with Darcy–Forchheimer flow	2
Issue Information	2
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	2
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	2
Convergence analysis of the splitting method to the nonlinear heat equation	2
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	2
A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions	2
Mixed convection of ferrofluids in a square enclosure with obstacles: Effect of iso‐perimetric shapes	2
	2
On the application of a Krylov subspace spectral method to poroacoustic shocks in inhomogeneous gases	2
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	2
A kernel‐based pseudo‐spectral method for multi‐term and distributed order time‐fractional diffusion equations	2
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	2
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	2
Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	2
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	2
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	2
	2
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	2
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	2
Convective thermal conditions and the thermophoretic effect's impacts on a hybrid nanofluid over a moving thin needle	2
	2
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	2
A virtual element method‐based positivity‐preserving conservative scheme for convection–diffusion problems on polygonal meshes	1
An explicit order 2 scheme for the strong approximation of Stratonovich stochastic differential equations with scalar noise	1
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	1
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	1
TheBDF2 FDMfor the fourth‐order equations with the multi‐termR‐Lfractional integral kernels	1
Discontinuous Galerkin finite element method for dynamic viscoelasticity models of power‐law type	1
	1
Controllability of nonlinear Hilfer fractional Langevin dynamical system	1
Three dimensional high order finite volume element schemes for elliptic equations	1
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	1
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	1
Finite element analysis of the singularly perturbed parabolic reaction‐diffusion problems with retarded argument	1
Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
A C0 interior penalty method for the phase field crystal equation	1
Issue Information	1
Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators	1
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	1
Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization	1
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	1
Issue Information	1
Convergence, bounded variation properties and Kruzhkov solution of a fully discrete Lagrangian–Eulerian scheme via weak asymptotic analysis for 1D hyperbolic problems	1
	1
Primal‐dual active set algorithm for valuating American options under regime switching	1
Conforming finite element method for the time‐fractional nonlinear stochastic fourth‐order reaction diffusion equation	1
Numerical methods for scattering problems from multi‐layers with different periodicities	1
Orthogonal polynomial bases in the mixed virtual element method	1
Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density	1
	1
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	1
A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model	1
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion	1

Positivity‐preserving scheme without separated method for 2D convection–diffusion equations on polygonal meshes	1
Issue Information	1
Issue Information	1
On numerical study of constrained coupled shape optimization problems based on a new shape derivative method	1
Pulsatile Darcy flow of water‐based thermally radiative carbon nanotubes between two concentric cylinders	1
A numerical scheme for the optimal control of groundwater pollution	1
Issue Information	1
High order accurate method for the numerical solution of the second order linear hyperbolic telegraph equation	1
Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation	1
Issue Information	1
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	1
A quartic trigonometric tension B‐spline finite element method for solving Gardner equation	1
Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	1
A spectral collocation method for a nonlinear multidimensional Volterra integral equation	1
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	1
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	1
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	1
Strong optimal error estimates of discontinuous Galerkin method for multiplicative noise driving nonlinear SPDEs	1
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions	1
Issue Information	1
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	1
A class of one‐parameter alternating direction implicit methods for two‐dimensional wave equations with discrete and distributed time‐variable delays	1
Numerical analysis for a class of coupled system of singularly perturbed time‐dependent convection‐diffusion equations with a discontinuous source term	1
	1
A minimax algorithm based on Newton's method and an application for finding multiple solutions of p‐area problems	1
Analysis of sparse recovery for Legendre expansions using envelope bound	1
P1$$ {P}_1 $$‐nonconforming quadrilateral finite element space with periodic boundary conditions: Part II. Application to the nonconforming heterogeneous multiscale method	1
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	1
Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system	1
	1
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	0
	0
Decoupled and linearized scalar auxiliary variable finite element method for the time‐dependent incompressible magnetohydrodynamic equations: Unconditional stability and convergence analysis	0
On the optimality of voronoi‐based column selection	0
A linear adaptive second‐order backward differentiation formulation scheme for the phase field crystal equation	0
Issue Information	0
A discontinuous least squares finite element method for the Helmholtz equation	0
	0
Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	0
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	0
On the compact difference scheme for the two‐dimensional coupled nonlinear Schrödinger equations	0
Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws	0
A second‐order time discretizing block‐centered finite difference method for compressible wormhole propagation	0
A two‐grid finite element method for the Allen‐Cahn equation with the logarithmic potential	0
Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves	0
Magnetohydrodnamics nanofluid flow of shaped nanoparticles over a porous stretching wall and slip effect	0
Error estimate of a finite element method for an optimal control problem with corner singularity using the stress intensity factor	0
Learning parameters of a system of variable order fractional differential equations	0
Error bound of the multilevel fast multipole method for 3‐D scattering problems	0
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	0
Robust Error Estimates for Second‐Order Stabilization Finite Element Method for Navier–Stokes Equations With Small Viscosity and Nonsmooth Initial Data	0
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	0
Computability of magnetic Schrödinger and Hartree equations on unbounded domains	0
Solving the2Dand3Dnonlinear inverse source problems of elliptic type partial differential equations by a homogenization function method	0
	0
Anderson acceleration for a regularized Bingham model	0
	0
Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem	0
A new ϕ‐FEM approach for problems with natural boundary conditions	0
	0
Optimal convergence rates for Galerkin approximation of operator Riccati equations	0
Numerical results for a fourth‐order nonlinear wave equation of Kirchhoff type with a viscoelastic term	0
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	0
Iteration acceleration methods for solving three‐temperature heat conduction equations on distorted meshes	0
A variable‐step high‐order scheme for time‐fractional advection‐diffusion equation with mixed derivatives	0
On the convergence of 2D P4+$$ {P}_{4+} $$ triangular and 3D P6+$$ {P}_{6+} $$ tetrahedral divergence‐free finite elements	0
Error analysis of a fully discrete projection method for magnetohydrodynamic system	0
Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint	0
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	0
Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature	0
A posteriori element residual error estimations for the cell functional minimization scheme	0
A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	0
An a posteriori error analysis for an augmented discontinuous Galerkin method applied to Stokes problem	0
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	0
Simulation of the interaction of light with 3‐D metallic nanostructures using a proper orthogonal decomposition‐Galerkin reduced‐order discontinuous Galerkin time‐domain method	0
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	0
	0
Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential	0
Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations	0
Issue Information	0
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	0
Exponential time difference methods with spatial exponential approximations for solving boundary layer problems	0
Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon	0
Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media	0
Issue Information	0
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	0
Error estimates for completely discrete FEM in energy‐type and weaker norms	0
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	0
Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid	0
Numerical approximation of solutions of the equations of quasistatic electroporoelasticity	0
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	0
Partial differential integral equation model for pricing American option under multi state regime switching with jumps	0
A C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients	0
Error bounds of fourth‐order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime	0
An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations	0